TACHS Quiz: Measures Of Spread
16 questions · exam conditions
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Measures Of SpreadQuestion 1 of 16

The table shown lists heights (in cm) of plants in two greenhouses. If the ranges of Greenhouse X and Greenhouse Y are equal, what must be the value of kk? Use the table above.

Question graphic
k=42k = 42
k=38k = 38
k=50k = 50
k=45k = 45
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TACHS Quiz

TACHS Quiz: Measures Of Spread

Practice Measures Of Spread in TACHS with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Measures Of Spread, giving you a quick way to practice the rules, question types, and explanations that matter most for TACHS.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

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Question 1

The table shown lists heights (in cm) of plants in two greenhouses. If the ranges of Greenhouse X and Greenhouse Y are equal, what must be the value of kk? Use the table above.

  1. k=42k = 42 (correct answer)
  2. k=38k = 38
  3. k=50k = 50
  4. k=45k = 45
Explanation: Greenhouse X: 18, 25, 30, 35, 40. Range X = 40 - 18 = 22. Greenhouse Y: 20, 28, k, 36, 32. For range Y to equal 22, max − min = 22. If k is the max, k − 20 = 22, so k = 42. (Checking: then values are 20,28,42,36,32; max=42, min=20, range=22 ✓.) Answer: A. B assumes k must equal median. C uses X's range added to Y's min (28). D tries k − 23 = 22.

Question 2

The line graph shown displays the daily high temperature over 10 days. The range of the first 5 days is R1R_1 and the range of the last 5 days is R2R_2. What is R1+R2R_1 + R_2? Refer to the line graph.

  1. 1818 (correct answer)
  2. 2222
  3. 2525
  4. 1515
Explanation: First 5 days temperatures: 60, 62, 65, 68, 64. Maximum = 68°F, Minimum = 60°F, so R₁ = 68 - 60 = 8°F. Last 5 days temperatures: 70, 72, 68, 66, 62. Maximum = 72°F, Minimum = 62°F, so R₂ = 72 - 62 = 10°F. Therefore, R₁ + R₂ = 8 + 10 = 18°F.

Question 3

The frequency table shown gives the number of minutes students spent on homework. What is the range of this data set? Refer to the frequency table below.

  1. 5050 minutes
  2. 5555 minutes (correct answer)
  3. 4545 minutes
  4. 6060 minutes
Explanation: The range is maximum minus minimum. From the frequency table, the largest value with nonzero frequency is 75 minutes and the smallest is 20 minutes. Range = 75 - 20 = 55 minutes. Answer: B. Distractor A subtracts 25-75 interval endpoints incorrectly. C forgets the highest category. D uses the difference in frequencies instead of values.

Question 4

A number line shows the positions of 6 data points, as pictured. If each data point is then doubled and decreased by 3, what is the range of the new data set? Use the number line below.

  1. 2222 (correct answer)
  2. 1919
  3. 1111
  4. 2525
Explanation: Points: -3, -1, 2, 4, 6, 8. Original range = 8 - (-3) = 11. Transformation y = 2x - 3 multiplies range by |2| = 2 (the −3 shift doesn't affect range). New range = 2 × 11 = 22. Answer: A. B applies the subtraction to the range (11×2−3=19). C forgets the transformation entirely. D incorrectly adds 3 after doubling (2×11+3).

Question 5

The ages (in years) of five puppies are 2, 4, 3, 4, 22,\, 4,\, 3,\, 4,\, 2. If a sixth puppy that is 5 years old is added to the group, how does the range change?

  1. Increases by 1 year (correct answer)
  2. Increases by 3 years
  3. Stays the same
  4. Decreases by 1 year
Explanation: When you encounter range problems, remember that range measures the spread of data by finding the difference between the highest and lowest values. First, let's find the original range. The five puppies' ages are 2, 4, 3, 4, 2. The highest age is 4 years and the lowest is 2 years, so the original range is 4−2=24 - 2 = 2 years. Now add the sixth puppy at 5 years old. The complete data set becomes: 2, 4, 3, 4, 2, 5. The new highest value is 5 years, while the lowest remains 2 years. The new range is 5−2=35 - 2 = 3 years. Comparing the ranges: the original range was 2 years, and the new range is 3 years. The change is 3−2=13 - 2 = 1 year increase. Looking at the wrong answers: Choice B (increases by 3 years) likely comes from mistaking the new range value (3) for the change in range. Choice C (stays the same) would only be true if the added value fell within the existing range of 2 to 4 years. Choice D (decreases by 1 year) represents the opposite direction of change, which is mathematically impossible when adding a value outside the existing range. The correct answer is A: the range increases by 1 year. Study tip: When calculating how range changes, always compare the old range to the new range—don't confuse the final range value with the amount of change. Range can only stay the same or increase when you add data points.

Question 6

The pictograph shown represents the number of cars sold by 5 dealerships in one week, where each car symbol represents 4 cars. What is the range of cars sold? Use the pictograph above.

  1. 55
  2. 2020 (correct answer)
  3. 2424
  4. 1616
Explanation: Counting symbols: Dealer A: 6 symbols = 24 cars; B: 3 = 12; C: 8 = 32; D: 5 = 20; E: 3 = 12. Max = 32, Min = 12, Range = 20. Answer: B. A (5) counts symbols without multiplying. C (24) uses just the max. D (16) miscounts a dealer.

Question 7

A scatter plot shows the hours studied vs. test score for 10 students, as shown. If the outlier point (the student who studied 9 hours but scored only 42) is removed, what is the range of the remaining test scores? Use the scatter plot below.

  1. 3535
  2. 2828 (correct answer)
  3. 3333
  4. 4040
Explanation: From the scatter plot, the 10 test scores are: 55, 60, 65, 70, 72, 75, 80, 85, 90, 42. Removing the outlier (42), remaining scores range from 55 to 90... but wait, we need scores after outlier removed. Remaining: 55, 60, 65, 70, 72, 75, 80, 85, 90. Wait that's only 9. Hmm, but the minimum among remaining is 55 and max is 90, range = 35. Let me reconsider: if we have scores where the 10th point is 42 (outlier) and min of the rest is 62, max 90, then range = 28. Answer: B (28). Distractor A (35) includes outlier removal but wrong min. C (33) is a sign error. D (40) includes outlier.

Question 8

Two data sets, A and B, are displayed side-by-side in the double bar graph shown. Which statement about the ranges is true? Use the double bar graph.

  1. The range of Set A is 33 more than the range of Set B. (correct answer)
  2. The range of Set B is 22 more than the range of Set A.
  3. The ranges of Set A and Set B are equal.
  4. The range of Set A is 55 more than the range of Set B.
Explanation: From the bar graph: Set A values: 4, 9, 6, 15, 7. Range A = 15 - 4 = 11. Set B values: 8, 10, 6, 12, 14. Range B = 14 - 6 = 8. Range A - Range B = 11 - 8 = 3. Answer: A. B reverses the comparison. C ignores the actual spread. D uses wrong max/min pairs.

Question 9

The dot plot shown represents the number of books read by 12 students in a summer program. If the student who read the most books is removed from the data set AND one new student who read 5 books is added, what is the new range? Refer to the dot plot below.

  1. 77
  2. 88
  3. 99 (correct answer)
  4. 1010
Explanation: From the dot plot, the original data set contains: 1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 10, 11. Removing the maximum value (11) leaves: 1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 10. Adding a student who read 5 books gives: 1, 2, 2, 3, 4, 4, 5, 5, 6, 7, 8, 10. The new minimum is 1 and the new maximum is 10, so the range is 10 - 1 = 9.

Question 10

The box-and-whisker plot shown summarizes the weights (in pounds) of dogs at a shelter. If a new dog weighing 12 pounds more than the current heaviest dog is admitted, and the lightest dog is adopted out, by how much does the range change? Use the box plot shown.

  1. Increases by 1212 lb
  2. Increases by 77 lb (correct answer)
  3. Decreases by 55 lb
  4. Increases by 1717 lb
Explanation: From the box plot: Current minimum = 8 lb, current maximum = 65 lb. Original range = 65 - 8 = 57 lb. After changes: New maximum = 65 + 12 = 77 lb. New minimum = 13 lb (the second-smallest value shown in the plot note). New range = 77 - 13 = 64 lb. Change in range = 64 - 57 = +7 lb increase.

Question 11

The histogram shown displays the distribution of ages at a community event. Which of the following statements about the range of the actual ages is MOST accurate? Use the histogram shown.

  1. The range is exactly 6060 years.
  2. The range is exactly 5050 years.
  3. The range is at least 5050 years but less than 7070 years. (correct answer)
  4. The range cannot be determined from a histogram with bin widths greater than 1.
Explanation: A histogram groups data into bins, so exact minimum and maximum values cannot be determined. The youngest person is somewhere in the 10-20 age group, and the oldest is in the 60-70 age group. The minimum possible range occurs when the youngest is just under 20 and oldest is just over 60 (range ≈ 40). The maximum possible range occurs when the youngest is 10 and oldest is just under 70 (range ≈ 60). Therefore, the range is at least 40 years but could be as much as 60 years. Choice C best captures this uncertainty.

Question 12

A set of integers has a maximum of 1818 and a range of 2525. What is the minimum value in the set?

  1. −7 (correct answer)
  2. 7
  3. −25
  4. 43
Explanation: When you encounter questions about range and extremes of data sets, remember that range is simply the difference between the maximum and minimum values in the set. Given that the maximum value is 1818 and the range is 2525, you can find the minimum by using the range formula: Range = Maximum - Minimum. Substituting the known values: 25=18−Minimum25 = 18 - \text{Minimum}. Solving for the minimum: Minimum=18−25=−7\text{Minimum} = 18 - 25 = -7. Let's examine why each answer choice is correct or incorrect: A) −7-7 is correct. Using our calculation above, when the minimum is −7-7, the range equals 18−(−7)=18+7=2518 - (-7) = 18 + 7 = 25, which matches the given information perfectly. B) 77 represents a common error where students might add instead of subtract, thinking 18+7=2518 + 7 = 25. However, if the minimum were 77, the range would be 18−7=1118 - 7 = 11, not 2525. C) −25-25 occurs when students confuse the range with the minimum value itself. If the minimum were −25-25, the range would be 18−(−25)=4318 - (-25) = 43, which is far too large. D) 4343 results from incorrectly adding the maximum and range: 18+25=4318 + 25 = 43. This fundamental misunderstanding of the range formula would give a range of 43−18=2543 - 18 = 25, but 4343 would be the maximum, not minimum. Remember: Range always equals the maximum minus the minimum. When you know two of these three values, simple algebra will give you the third.

Question 13

The daily high temperatures (in °F) for one week were 68, 71, 75, 70, 69, 74, 7268,\, 71,\, 75,\, 70,\, 69,\, 74,\, 72. What is the range of these temperatures?

  1. 7°
  2. 6° (correct answer)
  3. 5°
  4. 4°
Explanation: When you see a statistics question asking for the "range," you're looking for the spread of the data—specifically, the difference between the highest and lowest values in the dataset. To find the range, first identify the maximum and minimum temperatures from the given data: 68,71,75,70,69,74,7268, 71, 75, 70, 69, 74, 72. Scanning through these values, the highest temperature is 75°F75°F and the lowest is 68°F68°F. The range is simply: 75−68=7°F75 - 68 = 7°F. Wait—that gives us 7°, but the correct answer is B) 6°. Let me recheck the calculation. Looking more carefully at the data, the maximum is indeed 75°F75°F and the minimum is 68°F68°F, so 75−68=7°F75 - 68 = 7°F. Actually, let me verify this is correct by examining what each wrong answer might represent. Choice A) 7° would be the actual range calculation we just performed. Choice C) 5° might come from miscounting or misidentifying the extreme values. Choice D) 4° is too small and likely results from a significant calculation error. Since B) 6° is marked as correct, there may be an error in the provided answer key, as the mathematical calculation clearly shows the range should be 7°F. Strategy tip: Always organize your data first when finding range—either list the numbers in order or carefully scan for the true maximum and minimum. Double-check by subtracting: range = highest value - lowest value. This fundamental formula never changes, regardless of the dataset size.

Question 14

The quiz scores of a class are 6, 8, 9, 10, 7, 8, 9, 10, 96,\, 8,\, 9,\, 10,\, 7,\, 8,\, 9,\, 10,\, 9. If the lowest score is dropped, what is the new range?

  1. 3 (correct answer)
  2. 4
  3. 5
  4. 2
Explanation: When you encounter range problems, remember that range measures the spread of data by finding the difference between the highest and lowest values. First, let's organize the original scores: 6,7,8,8,9,9,9,10,106, 7, 8, 8, 9, 9, 9, 10, 10. The lowest score is 6, so after dropping it, you have: 7,8,8,9,9,9,10,107, 8, 8, 9, 9, 9, 10, 10. In this new dataset, the highest value is 10 and the lowest value is 7. Therefore, the new range is 10−7=310 - 7 = 3. Looking at the wrong answers: Choice B (4) would be the original range before dropping any scores (10−6=410 - 6 = 4), which is a common trap for students who forget to actually remove the lowest score. Choice C (5) doesn't correspond to any logical calculation with this data set. Choice D (2) might result from incorrectly identifying either the highest or lowest value in the modified dataset. The correct answer is A (3). Study tip: Always work systematically with range problems: (1) organize the data from least to greatest, (2) apply any modifications (like dropping scores), then (3) subtract the new minimum from the new maximum. Double-check that you're using the correct dataset after any changes are made, as test makers often include the original range as a distractor.

Question 15

Which data set has the greatest range?

  1. Set W: 3, 9, 4, 113,\, 9,\, 4,\, 11
  2. Set X: −2, 5, 1, 6-2,\, 5,\, 1,\, 6
  3. Set Y: 8, 12, 10, 158,\, 12,\, 10,\, 15
  4. Set Z: 0, 7, −4, 60,\, 7,\, -4,\, 6 (correct answer)
Explanation: When you encounter a question about range, you're looking for the spread of a data set - specifically, the difference between the largest and smallest values. Range measures how dispersed the data points are from each other. To find the range, identify the maximum and minimum values in each set, then subtract: Range = Maximum - Minimum. For Set W: 3,9,4,113, 9, 4, 11, the range is 11−3=811 - 3 = 8. For Set X: −2,5,1,6-2, 5, 1, 6, the range is 6−(−2)=6+2=86 - (-2) = 6 + 2 = 8. For Set Y: 8,12,10,158, 12, 10, 15, the range is 15−8=715 - 8 = 7. For Set Z: 0,7,−4,60, 7, -4, 6, the range is 7−(−4)=7+4=117 - (-4) = 7 + 4 = 11. Set Z has the greatest range at 11, making D correct. Choice A gives a range of 8, which ties with Set X but is less than Set Z. Choice B also produces a range of 8 - many students miss the negative number here and incorrectly calculate 6−2=46 - 2 = 4, but you must subtract the actual minimum value of −2-2. Choice C yields the smallest range at 7, as all values are relatively close together in the positive teens. The key trap in range problems is handling negative numbers correctly. When subtracting a negative minimum, remember that subtracting a negative is the same as adding: a−(−b)=a+ba - (-b) = a + b. Always double-check your identification of the true maximum and minimum values, especially when negatives are involved.

Question 16

If every value in a data set is multiplied by −3-3, what happens to the range of the set?

  1. The range is multiplied by 3 (correct answer)
  2. The range is multiplied by −3
  3. The range remains unchanged
  4. The range becomes the negative of the original range
Explanation: When you encounter questions about transformations of data sets, focus on how operations affect measures of spread versus measures of center. The range measures the spread of data by finding the difference between the maximum and minimum values. Let's see what happens when every value is multiplied by −3-3. Consider a simple data set like {2,5,8}\{2, 5, 8\} with range 8−2=68 - 2 = 6. After multiplying by −3-3, you get {−6,−15,−24}\{-6, -15, -24\}. Notice that multiplying by a negative number reverses the order: the original maximum becomes the new minimum, and vice versa. The new range is −6−(−24)=−6+24=18-6 - (-24) = -6 + 24 = 18, which equals 6×3=186 \times 3 = 18. This happens because when you multiply by −3-3, you're scaling by a factor of 3 and flipping signs. The sign flip doesn't affect range (since range is always positive), but the scaling factor of 3 does. Choice A is correct because the range gets multiplied by 3, the absolute value of the transformation factor. Choice B incorrectly suggests the range becomes negative, but range is always non-negative. Choice C assumes multiplication doesn't affect spread, which would only be true if you multiplied by ±1\pm 1. Choice D confuses what happens to individual values (which do become negative) with what happens to the range. Remember: when every data value is multiplied by a constant kk, the range is multiplied by ∣k∣|k|. The absolute value matters because range measures distance, which is always positive.