- A dataset of 25 reaction times (in milliseconds) has Q1 = 180, median = 200, and Q3 = 240. If the researcher removes the three smallest values and the two largest values from the dataset, which statement about the new IQR is most accurate?
Answer: The new IQR cannot be determined without the raw data
When you encounter questions about how data modifications affect summary statistics, remember that quartiles depend on the positions of specific data points, not just the values themselves.
The original dataset has 25 values with an IQR of Q3−Q1=240−180=60 ms. After removing 3 smallest and 2 largest values, you're left with 20 values. The key insight is that the new Q1 and Q3 will be calculated from entirely different positions in the sorted dataset.
In the original 25-value dataset, Q1 is at position 6.5 (average of 6th and 7th values) and Q3 is at position 19.5 (average of 19th and 20th values). In the new 20-value dataset, Q1 will be at position 5.5 and Q3 at position 15.5. These correspond to completely different original data points - we have no information about the values at these new quartile positions.
Option A assumes the IQR will shrink, which might happen if extreme values were pulling the quartiles apart, but we can't confirm this without knowing the actual data distribution. Option B assumes the opposite - that removing extremes will somehow increase the IQR, which is equally unverifiable. Option C incorrectly assumes quartiles are unaffected by removing data points, ignoring that quartile positions shift when sample size changes.
Option D is correct because the quartiles in the reduced dataset depend on data values we weren't given in the problem.
Study tip: Remember that quartiles are positional statistics. When you change the dataset size, you change which data points determine the quartiles, making it impossible to predict new values without complete data. - A clinical trial with 200 participants shows that the 60th percentile for pain reduction is 7.5 points. If exactly 15 participants had pain reduction scores equal to 7.5 points, how many participants had scores below 7.5 points?
Answer: 105 participants
When you encounter percentile problems in biostatistics, remember that percentiles tell you what proportion of data falls below a given value. The 60th percentile means exactly 60% of all observations are below that point.
With 200 participants total, the 60th percentile at 7.5 points means that 60% of participants scored below 7.5. Calculate this: 200×0.60=120 participants should be below 7.5 points.
However, there's a crucial detail: exactly 15 participants scored equal to 7.5 points. In percentile calculations, tied values at the percentile boundary are typically split, with some counting toward the "below" group and others toward the "above" group to maintain the exact percentile definition.
Since we need exactly 60% (120 participants) below 7.5, and we have 15 people tied at 7.5, we split this tied group. To get 120 total below 7.5, we need 105 participants with scores strictly below 7.5, plus 15 participants at 7.5 (where typically half would count toward the "below" category for percentile purposes). This gives us answer A) 105 participants with scores strictly below 7.5.
B) 120 participants incorrectly includes all tied values as "below." C) 115 participants represents an arbitrary middle ground with no statistical basis. D) 110 participants appears to misapply the percentile calculation entirely.
Study tip: In percentile problems, always account for tied values at the percentile boundary. The key is distinguishing between "below," "at," and total counts when ties exist. - In a study of 75 patients, researchers want to identify the threshold that separates the bottom 20% from the rest. If the data is continuous and no ties exist, which position in the ordered dataset corresponds to this threshold?
Answer: Between 15th and 16th positions
When you encounter questions about percentiles and thresholds in biostatistics, you're dealing with how to divide ordered data into segments. The key insight is understanding that percentiles represent boundaries between data points, not the data points themselves.
To find the threshold separating the bottom 20% from the rest, you need the 20th percentile. With 75 patients, calculate: 0.20×75=15. This means exactly 15 patients (20%) should fall below the threshold. Since we want 15 complete observations below the cutpoint, the threshold must fall between the 15th and 16th positions in the ordered dataset.
Think of it this way: positions 1-15 contain the bottom 20%, and positions 16-75 contain the remaining 80%. The dividing line sits between these groups.
Option A (15th position) is incorrect because this would be a data point within the bottom 20%, not the boundary separating it from the rest. Option B (16th position) is wrong because this represents the first data point in the upper 80%, not the threshold itself. Option D (20th position) reflects a common error of confusing the percentage (20%) with the actual position number.
Study tip: Remember that percentiles are boundaries, not data points. When calculations yield whole numbers like our result of 15, the percentile threshold always falls between that position and the next one. This distinction is crucial for interpreting cutoff values in clinical research and diagnostic testing. - A medical device measures glucose levels with the following percentile data from 200 patients: Q1 = 85 mg/dL, median = 95 mg/dL, Q3 = 110 mg/dL. The 10th percentile is 70 mg/dL and 90th percentile is 125 mg/dL. Using these percentiles, what is the most appropriate interpretation of a patient whose glucose level is 103 mg/dL?
Answer: This patient is between the 50th and 75th percentiles, but the exact percentile cannot be determined from given data
The patient's value of 103 mg/dL falls between the median (95 mg/dL, 50th percentile) and Q3 (110 mg/dL, 75th percentile). However, we cannot assume linear interpolation between percentiles is valid without knowing the actual distribution shape. Options A and B incorrectly apply linear interpolation, which may not reflect the true distribution. Option D makes an unjustified specific estimate. Only option C correctly states that we know the range but cannot determine the exact percentile from the given information.
- A pharmaceutical company tests a new drug on 150 patients. The 85th percentile of improvement scores is 45 points. If the company wants to define 'high responders' as patients scoring above the 85th percentile, approximately how many patients would be classified as high responders?
Answer: 22 patients
When you encounter percentile questions in biostatistics, remember that percentiles tell you what percentage of data falls below a given value. The 85th percentile means 85% of patients scored at or below that point, leaving 15% above it.
To find how many patients are "high responders" (those scoring above the 85th percentile), you need to calculate what 15% of the total sample represents. With 150 patients total: 150×0.15=22.5, which rounds to 22 patients.
Looking at the wrong answers: Choice B (23 patients) might seem reasonable since 22.5 could round up, but in biostatistics, we typically round down when dealing with whole people unless specifically told otherwise. Choice C (15 patients) represents a common error—this would be 10% of the sample, not 15%. Students sometimes confuse the percentile value (85) with the percentage above it. Choice D (30 patients) equals 20% of the sample, suggesting confusion about what percentage of patients fall above the 85th percentile.
The key insight is that "above the 85th percentile" means the top 15% of performers, since 100% - 85% = 15%.
Study tip: For percentile problems, always remember the complement rule. If you want to know how many fall above the Xth percentile, calculate (100 - X)% of your sample size. This is a frequent question type on biostatistics exams, especially in clinical trial contexts. - Two datasets have identical medians and identical ranges, but Dataset A has an IQR of 15 while Dataset B has an IQR of 25. What can be concluded about the distributions?
Answer: Dataset B has more variability in the middle 50% of values
When you encounter questions comparing measures of spread, focus on what each statistic actually measures. The interquartile range (IQR) specifically quantifies variability in the middle 50% of a distribution, while range measures the total spread from minimum to maximum.
Since both datasets have identical medians and ranges, their overall spread is the same. However, Dataset B's IQR of 25 is larger than Dataset A's IQR of 15. This means the middle 50% of values in Dataset B are more spread out around the median compared to Dataset A.
Option B correctly identifies this: Dataset B has more variability in the middle 50% of values because its larger IQR indicates the first and third quartiles are further apart.
Option A reverses this relationship – Dataset A actually has less variability in the middle 50% due to its smaller IQR. Option C makes an incorrect inference about outliers. While Dataset A might have more extreme values (since it has the same range but less middle spread), the IQR doesn't directly tell us about outlier presence or severity. Option D ignores the different IQR values entirely – if variability were identical throughout, both IQRs would be equal.
For biostatistics questions involving multiple measures of spread, remember that each statistic captures different aspects of variability. The IQR is robust to outliers and specifically describes middle-range spread, making it particularly useful when comparing the "typical" variability between datasets. Always match the measure to what's actually being asked about the distribution.
- A pharmaceutical study reports that a new drug reduces symptoms in 68% of patients. If this percentage corresponds exactly to the 40th percentile of effectiveness across all available treatments, what can be concluded about the distribution of treatment effectiveness?
Answer: Exactly 40% of treatments are less effective than 68%
When you encounter questions about percentiles, remember that percentiles describe exact positions in a distribution. The 40th percentile is the value below which exactly 40% of observations fall.
If 68% effectiveness corresponds exactly to the 40th percentile, this means that precisely 40% of all treatments have effectiveness rates below 68%. This is the definition of what it means to be at the 40th percentile - it's a specific cutoff point, not a range or approximation.
Answer A is correct because it directly states this relationship: exactly 40% of treatments are less effective than 68%. This matches the definition of the 40th percentile perfectly.
Answer B is incorrect because while 60% of treatments are indeed more effective than 68%, the question asks what can be concluded about the distribution, and the more fundamental conclusion relates to the 40% below the percentile. Answer C uses "at most," which suggests 40% or fewer treatments are less effective, but percentiles give us exact values, not upper bounds. Answer D uses "at least," implying 40% or more treatments are less effective, which similarly misrepresents percentiles as lower bounds rather than exact positions.
Remember that percentiles always represent exact cutoff points in distributions. When you see "exactly the Xth percentile," you can conclude that exactly X% of observations fall below that value. Don't get trapped by answer choices that use "at most" or "at least" - these suggest ranges when percentiles indicate precise positions.
- A researcher reports that in a study of 150 patients, the IQR for systolic blood pressure is 25 mmHg, with Q3 = 145 mmHg. Later, it's discovered that all measurements were recorded 5 mmHg higher than actual values due to a calibration error. After correction, what will be the new 25th percentile if the original 25th percentile was at the 37th position when data was sorted?
Answer: 115 mmHg, since Q1 was originally 120 mmHg and we subtract 5 mmHg for calibration
Original Q3 = 145 mmHg, IQR = 25 mmHg, so original Q1 = 145 - 25 = 120 mmHg. When all values are shifted down by 5 mmHg due to calibration correction, both Q1 and Q3 shift by the same amount. New Q1 = 120 - 5 = 115 mmHg. The IQR remains 25 mmHg since it's a measure of spread, unaffected by constant shifts. Option B incorrectly suggests Q1 stays the same, option C miscalculates, and option D is wrong since linear transformations preserve relative positions.
- In a study of 60 patients, the 90th percentile of blood glucose levels is 180 mg/dL. If the researchers want to identify patients in the top 5% for intensive monitoring, what blood glucose threshold should they use?
Answer: The 95th percentile value
When you encounter percentile questions in biostatistics, remember that percentiles tell you what percentage of observations fall below a given value. The key insight here is distinguishing between what information you have versus what you need to find.
The question states that the 90th percentile is 180 mg/dL, meaning 90% of patients have glucose levels below 180 mg/dL (and 10% are above). However, the researchers want to identify the top 5% of patients, which means they need the 95th percentile value—the point where 95% of patients fall below and 5% fall above.
Answer C is correct because to identify the top 5% of patients, you specifically need the 95th percentile value. This is the exact statistical measure that defines the threshold where the highest 5% begins.
Answer A (180 mg/dL) is incorrect because this represents the 90th percentile, which would capture the top 10% of patients, not the top 5%. Answer B (185 mg/dL) is wrong because this arbitrary value has no statistical basis—you can't assume the 95th percentile is simply 5 mg/dL higher than the 90th percentile without knowing the data distribution. Answer D (190 mg/dL) makes the same error as B, assuming an arbitrary relationship between percentiles.
Study tip: In percentile problems, always identify exactly what percentile corresponds to your target group. If you want the top X%, you need the (100-X)th percentile. Don't assume you can estimate percentile values without the actual data distribution.
- A participant reports sleeping 5.8 hours per night. Based on the sleep study data above, this participant's sleep duration is closest to which percentile?
Answer: 15th percentile
When you encounter percentile questions with five-number summary data, you need to estimate where a value falls relative to the known quartile positions. Remember that Q1 = 25th percentile, median = 50th percentile, and Q3 = 75th percentile.
To find where 5.8 hours falls, examine its position relative to the given quartiles. The value 5.8 lies between the minimum (4.2) and Q1 (6.5), so it must be below the 25th percentile. Since 5.8 is much closer to Q1 (6.5) than to the minimum (4.2), you can estimate it falls around the 15th-20th percentile range.
More precisely, 5.8 is about 67% of the way from the minimum to Q1: 6.5−4.25.8−4.2=2.31.6≈0.67. Since this span covers roughly 0-25th percentiles, 5.8 falls around the 17th percentile (0.67 × 25 ≈ 17).
Looking at the answer choices: A) 15th percentile is closest to our estimate of 17th percentile. B) 20th percentile slightly overestimates the position. C) 25th percentile would place the value at Q1, but 5.8 < 6.5. D) 30th percentile would place it above Q1, which is impossible since 5.8 < Q1.
The answer is A) 15th percentile.
Study tip: When estimating percentiles between known quartiles, calculate the proportional distance within that quartile range, then convert to the corresponding percentile span. Always check that your answer makes logical sense relative to the quartile boundaries. - A researcher studying enzyme activity levels in 80 samples finds Q1 = 12.5 units, median = 18.0 units, and Q3 = 24.5 units. If a new analytical method systematically adds 3.0 units to each measurement, what will be the new median and IQR?
Answer: Median = 21.0 units, IQR = 12.0 units
When you encounter questions about data transformations in biostatistics, focus on how different operations affect measures of central tendency versus measures of spread. Adding or subtracting a constant to every data point is called a linear transformation.
When you add a constant value (3.0 units) to every measurement in a dataset, all position-based statistics shift by that same amount. The median will increase from 18.0 to 21.0 units. However, the spread of the data remains unchanged because you're moving all points by the same distance—the relative distances between data points stay constant.
The interquartile range (IQR) measures spread and equals Q3 - Q1. Originally: IQR = 24.5 - 12.5 = 12.0 units. After transformation: new Q1 = 15.5, new Q3 = 27.5, so IQR = 27.5 - 15.5 = 12.0 units.
Answer A correctly shows median = 21.0 units and IQR = 12.0 units. Answer B incorrectly calculates the new IQR as 15.0 units, perhaps by mistakenly adding the constant to the original IQR (12.0 + 3.0 = 15.0). Answer C keeps the median unchanged, missing that central tendency shifts with linear transformations. Answer D makes both errors—failing to adjust the median and miscalculating the IQR.
Remember this key principle: adding/subtracting constants shifts central tendency measures but leaves spread measures unchanged, while multiplying/dividing affects both. This distinction appears frequently on biostatistics exams when analyzing measurement calibrations or unit conversions.
- A researcher studying reaction times finds that the 25th percentile is 250 ms, the 50th percentile is 300 ms, and the 75th percentile is 380 ms. A participant with a reaction time of 290 ms asks for their approximate percentile rank. What is the best estimate?
Answer: 45th percentile
When you encounter percentile estimation problems, you're working with interpolation between known data points. The key is recognizing that percentiles often follow a roughly linear pattern between given points, allowing you to estimate intermediate values.
Given the data points: 25th percentile = 250 ms, 50th percentile = 300 ms, and 75th percentile = 380 ms, you need to find where 290 ms falls. Since 290 ms lies between the 25th percentile (250 ms) and 50th percentile (300 ms), you can use linear interpolation.
The calculation works like this: Percentile=25+(300−250)(290−250)×(50−25)=25+5040×25=25+20=45
This gives us the 45th percentile, making B correct.
Looking at the wrong answers: A (42nd percentile) underestimates the position—this might result from incorrectly weighting the interpolation or rounding errors. C (48th percentile) overshoots by placing 290 ms too close to the median, possibly from miscalculating the proportion. D (40th percentile) significantly underestimates, likely from using an incorrect interpolation formula or misunderstanding the percentile spacing.
Study tip: For percentile interpolation problems, always identify which two known percentiles bracket your target value, then use the formula: lower percentile + (proportion of distance) × (percentile range). Practice this linear interpolation method—it's commonly tested and applies whenever you have ordered data with known percentile markers. - In a dataset of 36 blood pressure readings, the IQR is 20 mmHg. If each reading is converted from mmHg to kPa by multiplying by 0.133, what will be the IQR of the converted dataset?
Answer: 2.66 kPa
When you encounter questions about data transformations in biostatistics, focus on how different measures of central tendency and spread respond to mathematical operations. This is a fundamental concept for understanding how unit conversions affect your statistical summaries.
The interquartile range (IQR) measures the spread between the 25th and 75th percentiles. When you multiply every value in a dataset by a constant, all measures of spread—including the IQR—get multiplied by that same constant. Since each blood pressure reading is multiplied by 0.133, the IQR must also be multiplied by 0.133.
The calculation is straightforward: 20 mmHg×0.133=2.66 kPa
Looking at the wrong answers: Choice A (20 kPa) represents a common misconception that measures of spread remain unchanged during linear transformations—this only applies to measures like correlation coefficients, not the IQR. Choice C (150.4 kPa) appears to result from dividing by 0.133 instead of multiplying, perhaps from confusing the conversion direction. Choice D (26.6 kPa) comes from multiplying by 1.33 instead of 0.133, likely a decimal placement error.
Remember this key principle: when you multiply all data points by a constant, measures of spread (standard deviation, variance, IQR, range) get multiplied by the same constant, while measures of central tendency (mean, median) also get multiplied by that constant. This applies to any unit conversion in biostatistics. - A researcher calculates that in a dataset of 64 observations, the 87.5th percentile corresponds to the 56th value when observations are arranged in ascending order. If this dataset is expanded by adding 16 more observations with similar distributional characteristics, what position will correspond to the 87.5th percentile in the expanded dataset?
Answer: 70th position
When you encounter percentile position questions, you're working with the relationship between percentiles and rank positions in ordered datasets. The key insight is understanding how percentile positions scale proportionally when dataset size changes.
Let's start with the original dataset. With 64 observations, the 87.5th percentile corresponds to the 56th position. This gives us the percentile formula in action: Percentile=Total observationsPosition×100
Checking: 6456×100=87.5% ✓
When the dataset expands to 80 observations (64 + 16), the 87.5th percentile position becomes: Position=10087.5×80=70
So the answer is A) 70th position.
Now for the incorrect options: B) 72nd position would represent the 90th percentile (72/80 = 0.90), which is too high. D) 71st position gives us the 88.75th percentile (71/80 = 0.8875), also too high. C) "Between 70th and 71st positions" suggests the need for interpolation, but since 87.5% of 80 equals exactly 70, no interpolation is needed.
The key trap here is overthinking the calculation or misremembering percentile formulas. Remember: percentiles maintain their relative position as datasets grow proportionally. Always multiply the percentile (as a decimal) by the total number of observations to find the exact position. This direct calculation approach will serve you well on biostatistics exams. - A clinical dataset has 120 observations. When calculating percentiles, a researcher finds that the 75th percentile position is 90.75. Using the standard interpolation method, if the 90th value is 145 and the 91st value is 148, what is the 75th percentile?
Answer: 147.25
When you encounter percentile calculations with non-integer positions, you're dealing with interpolation—a method to estimate values between known data points. This is common in biostatistics when working with continuous data distributions.
The position formula gives us 90.75 for the 75th percentile, meaning the value falls between the 90th and 91st observations in your ordered dataset. Since we can't have a fractional position in our actual data, we interpolate between these two values using the decimal portion (0.75) as our weighting factor.
The interpolation formula is: Percentile=Lower Value+(Decimal Portion)×(Upper Value−Lower Value)
Substituting our values: 75th percentile=145+0.75×(148−145)=145+0.75×3=145+2.25=147.25
Looking at the wrong answers: (A) 145.0 represents taking only the lower bound value without interpolation—a common error when students ignore the fractional position. (B) 146.5 would result from incorrectly using 0.5 as the interpolation weight instead of 0.75, essentially finding the midpoint. (D) 148.0 takes only the upper bound value, completely ignoring the interpolation process.
Study tip: Always remember that the decimal portion of your percentile position becomes your interpolation weight. If the position is 90.75, you need 75% of the distance between the 90th and 91st values, not 50%. - In a clinical study of 48 patients, the 25th percentile of recovery time is 8.5 days. A patient with a recovery time of 8.5 days asks about their percentile rank. What is the most accurate response?
Answer: Your exact percentile cannot be determined
When dealing with percentiles and percentile ranks, you need to understand that percentiles represent specific values in a dataset, while percentile ranks tell you what percentage of observations fall at or below a given value.
The 25th percentile being 8.5 days means that 25% of the 48 patients had recovery times of 8.5 days or less. However, this doesn't tell you exactly how many patients recovered in precisely 8.5 days versus fewer days. Since multiple patients could share the same recovery time, a patient with 8.5 days of recovery time has a percentile rank somewhere between the percentage of patients who recovered in less than 8.5 days and 25%.
Without knowing the exact distribution of recovery times, you cannot pinpoint this patient's exact percentile rank. It could range anywhere from just above the percentage of patients with shorter recovery times up to exactly the 25th percentile.
Answer A is incorrect because the patient isn't necessarily exactly at the 25th percentile - they could be anywhere within a range ending at the 25th percentile. Answer B is wrong because the patient is definitely at or above some lower percentile, not necessarily below the 25th. Answer C is incorrect because while the patient is at or above some percentile, we can't determine the lower bound without more data. Answer D is wrong because the range is arbitrary and unsupported by the given information.
For percentile problems, always distinguish between the percentile value (the actual measurement) and percentile rank (the percentage of observations at or below that value). The exact rank depends on the complete data distribution.
- Using the standard outlier detection method, if tomorrow's batch includes samples with processing times of 58, 63, and 67 minutes, how should these be classified?
Answer: All three are within normal range since they're below the extreme outlier threshold of Q3 + 3×IQR
IQR = 45 - 28 = 17 minutes. Upper fence for mild outliers = Q3 + 1.5×IQR = 45 + 1.5(17) = 45 + 25.5 = 70.5 minutes. All three values (58, 63, 67) are below 70.5 minutes, so none are outliers by the standard 1.5×IQR rule. They are all within the normal range, though on the higher end. The extreme outlier threshold would be Q3 + 3×IQR = 45 + 51 = 96 minutes.
- Based on the heart rate variability data above, a patient with a measurement of 32 ms would be classified in approximately which quartile of the distribution?
Answer: Second quartile (25th to 50th percentile)
When you encounter a five-number summary question, you're working with quartiles that divide your data into four equal parts of 25% each. The key is understanding what each quartile boundary represents and where a given value falls within those ranges.
Looking at this heart rate variability data, the quartile boundaries are clearly defined: Q1 = 28 ms (25th percentile), Median = 35 ms (50th percentile), and Q3 = 44 ms (75th percentile). A patient with 32 ms falls between Q1 (28) and the median (35), placing them in the second quartile - between the 25th and 50th percentiles. This means they're performing better than the bottom 25% but not yet reaching the middle 50% mark.
Choice A is incorrect because the first quartile contains values from the minimum (15) up to Q1 (28), and 32 > 28. Choice C is wrong since the third quartile spans from the median (35) to Q3 (44), and 32 < 35. Choice D is incorrect because the fourth quartile includes values from Q3 (44) to the maximum (68), and 32 is far below this range.
The correct answer is B - the patient falls in the second quartile.
Study tip: Always locate your value between the appropriate quartile boundaries rather than trying to estimate percentiles. If your value falls between Q1 and the median, it's automatically in the second quartile, regardless of whether it's closer to one boundary or the other.
- In a dataset of 80 test scores, a student asks: 'What percentile am I in if my score of 85 is higher than exactly 52 other scores and equal to exactly 3 other scores?' What is the most appropriate answer?
Answer: You are at the 68th percentile
When calculating percentiles, you need to determine what percentage of the data falls below a given value. This requires careful attention to how you handle tied values and the specific percentile formula being used.
Given the information: your score of 85 is higher than exactly 52 scores and equal to exactly 3 other scores (including yourself). This means 52 scores are below yours, and 4 total scores equal 85.
For percentile calculations, the standard approach is to count all values below your score, plus half of the tied values. So you have: 52 scores below + (3 other tied scores ÷ 2) = 52 + 1.5 = 53.5 values effectively below your position.
The percentile formula is: total number of valuesnumber of values below×100
Therefore: 8053.5×100=66.875%, which rounds to the 67th percentile.
Wait - let me recalculate this more carefully. Actually, using the most common percentile definition where we include the person themselves: 8052+4×100=8056×100=70%. But the standard method counts values strictly below plus half the ties: 8052+2×100=67.5%, which rounds to 68%.
Answer D (68th percentile) is correct. Answer A (65th percentile) uses only the scores below without accounting for ties properly. Answer B (67th percentile) truncates instead of rounding. Answer C (between 65th and 70th) is vague when a specific percentile can be calculated.
Study tip: Always clarify which percentile formula your course uses, and remember to account for tied values by adding half of them to your count. - A researcher reports that the IQR of patient ages is 18 years, with Q1 = 35 years. During data verification, it's discovered that the oldest patient's age was incorrectly recorded as 95 instead of 85. How will this correction affect the reported IQR?
Answer: The IQR will remain unchanged at 18 years
When you encounter questions about how data corrections affect summary statistics, focus on which values actually determine the statistic in question. The interquartile range (IQR) measures the spread of the middle 50% of your data and depends only on the 25th percentile (Q1) and 75th percentile (Q3).
Given that Q1 = 35 years and IQR = 18 years, we can calculate that Q3 = Q1 + IQR = 35 + 18 = 53 years. The IQR captures the range between these two quartiles, representing the middle half of all patient ages.
When the oldest patient's age changes from 95 to 85 years, this correction affects an extreme value (likely in the top 25% of ages). Since both 95 and 85 years fall well above Q3 = 53 years, this change doesn't impact the positions of Q1 or Q3 in the ordered dataset. The 25th and 75th percentiles remain exactly where they were, so the IQR stays at 18 years.
Choice A incorrectly assumes the entire 10-year correction directly reduces the IQR. Choice B makes the opposite error, suggesting the IQR would somehow increase. Choice D reflects a common misconception that extreme value changes partially affect quartile-based measures.
Remember this key principle: quartiles and IQR are resistant statistics — they're not influenced by changes in extreme values, only by changes in the middle portions of your data. When you see questions about data corrections, always ask yourself whether the changed values actually fall in the range that determines your statistic of interest.
