Middle School Math Quiz: Measures Of Center And Variability
5 questions · exam conditions
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Measures Of Center And VariabilityQuestion 1 of 5

A teacher wants to remove one outlier from a data set of 20 test scores to reduce variability. The current data has a mean of 78 and MAD of 7.5. If she removes a score of 95, what will happen to the measures of center and variability?

The mean will decrease and MAD will decrease, making the remaining data less variable
The mean will decrease but MAD will increase due to having fewer data points
The mean will increase and MAD will decrease since the outlier is removed
The mean will remain approximately the same but MAD will decrease significantly
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Middle School Math Quiz

Middle School Math Quiz: Measures Of Center And Variability

Practice Measures Of Center And Variability in Middle School Math 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 Center And Variability, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

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.

All questions

Question 1

A teacher wants to remove one outlier from a data set of 20 test scores to reduce variability. The current data has a mean of 78 and MAD of 7.5. If she removes a score of 95, what will happen to the measures of center and variability?

  1. The mean will decrease and MAD will decrease, making the remaining data less variable (correct answer)
  2. The mean will decrease but MAD will increase due to having fewer data points
  3. The mean will increase and MAD will decrease since the outlier is removed
  4. The mean will remain approximately the same but MAD will decrease significantly
Explanation: Removing the high outlier (95) will decrease the mean since 95 is above the current mean of 78. The new mean will be (20×78 - 95)/19 = (1560 - 95)/19 ≈ 77.1. The MAD will also decrease because the extreme value that was contributing large deviations is removed, and the remaining values will have smaller average deviations from the new (lower) mean.

Question 2

A student calculated the mean of 12 test scores and got 84. She then realized she misread one score as 76 when it was actually 88. After correcting this error, she wants to find the mean absolute deviation of the corrected data set. If the original (incorrect) MAD was 5.2, what additional information does she need?

  1. She needs to know the median of the corrected data set to calculate the new MAD
  2. She needs to know all individual scores because MAD calculation requires the corrected mean (correct answer)
  3. She needs only the range of the data set since MAD is related to the range
  4. She needs no additional information since the MAD will increase by exactly 1 point
Explanation: The corrected mean will be 84 + (88-76)/12 = 84 + 1 = 85. To find the new MAD, she needs to calculate the absolute deviation of each score from this new mean of 85, then find the average of those absolute deviations. This requires knowing all individual scores, not just summary statistics.

Question 3

Two data sets each contain 15 values. Set A has a mean of 60 and MAD of 8. Set B has a mean of 60 and MAD of 12. If the data sets are combined into one set of 30 values, what can be determined about the combined set?

  1. The combined mean will be 60 and the combined MAD will be exactly 10
  2. The combined mean cannot be determined but the combined MAD will be approximately 10
  3. The combined mean will be greater than 60 and the combined MAD will be between 8 and 12
  4. The combined mean will be 60 but the combined MAD cannot be determined from given information (correct answer)
Explanation: When combining data sets, you need to understand how means and measures of variability behave differently. The mean has a predictable combining formula, but the Mean Absolute Deviation (MAD) does not. For the combined mean, you can calculate it directly. Since both sets have equal size (15 values each) and the same mean (60), the combined mean is simply the weighted average: 15×60+15×6030=60\frac{15 \times 60 + 15 \times 60}{30} = 60. When combining sets of equal size with the same mean, the combined mean equals that original mean. However, MAD measures how spread out the data points are from the mean. Even though both sets have the same mean and you know their individual MADs, you cannot determine the combined MAD without knowing the actual data values. The combined MAD depends on how the individual data points from both sets relate to the new combined mean, which requires the raw data. Answer A incorrectly assumes you can average the MADs (8 + 12 ÷ 2 = 10), but MAD doesn't combine this way. Answer B correctly notes that MAD cannot be precisely determined but wrongly claims the mean cannot be found. Answer C incorrectly suggests the mean would increase—there's no reason for this since both original means equal 60. Answer D correctly identifies that the combined mean can be calculated (it's 60) but the combined MAD cannot be determined from the given information alone. Study tip: Remember that means combine predictably using weighted averages, but measures of spread (like MAD or standard deviation) require the actual data values to calculate accurately when combining sets.

Question 4

A data set has 9 values with a median of 45 and an interquartile range of 12. If the smallest value is increased by 8 and the largest value is decreased by 3, which statement about the new data set is definitely true?

  1. The median will increase and the interquartile range will remain unchanged at 12
  2. The median will remain at 45 and the interquartile range will remain unchanged at 12 (correct answer)
  3. The median will remain at 45 but the interquartile range will decrease to less than 12
  4. The median will decrease and the interquartile range will increase to more than 12
Explanation: With 9 values, the median is the 5th value when ordered. Changing only the 1st (smallest) and 9th (largest) values doesn't affect the 5th value, so median stays 45. The IQR depends on Q1 (between 2nd and 3rd values) and Q3 (between 7th and 8th values), which are also unaffected by changes to the 1st and 9th values.

Question 5

The mean absolute deviation (MAD) of a data set is 6.4, and the mean is 52. If every value in the data set is multiplied by 1.5, what will be the new mean absolute deviation?

  1. 6.4, because multiplying by a constant doesn't change the MAD
  2. 8.9, because the MAD increases by the same factor as the mean
  3. 9.6, because the MAD is multiplied by the same scaling factor (correct answer)
  4. 4.27, because the MAD is divided by the scaling factor when data is multiplied
Explanation: When all data values are multiplied by a constant k, both the mean and the deviations from the mean are multiplied by k. Since MAD measures the average absolute deviation from the mean, it is also multiplied by k. Therefore, new MAD = 1.5 × 6.4 = 9.6.