How Data Changes Affect Center and Variation: Sample FAST Questions
Given a real-world scenario, students determine and describe how changes in data values impact measures of center (mean and median) and measures of variation (range and interquartile range). For example, they predict what happens to the mean when an outlier is added or a value is removed from a data set.
How the FAST tests this benchmark
FAST items are mostly multiple choice questions predicting or explaining how adding, removing, or changing a data value affects the mean, median, range, or IQR.
Skills students need
Describe the impact of data changes on measures of center
Describe the impact of data changes on measures of variation
Try 4 real MA.6.DP.1.6 questions
These come straight from Algebro's question bank. Pick an answer to check it instantly.
Question 1EasyMultiple Choice
A data set is: 50,58,65,72,80. The range is currently 30. If the maximum value changes from 80 to 100, what is the new range?
Correct answer: D. 50
This explanation shows one way to solve the problem.
New max and unchanged min: Max → 100. Min stays at 50.
New range: 100−50=50
Final Answer
50
Question 2MediumMultiple Choice
A data set is: 14,18,22,26,30. The mean is 22 and the median is 22. The value 30 is removed from the data set. Which measure of center is MORE affected?
Correct answer: B. Both are equally affected, each drops from 22 to 20
This explanation shows one way to solve the problem.
New mean (removing 30): Sum with 30 → ≈20 (was 22).
New median and comparison: Median: 20 (was 22). Mean changed 2.0 Median changed 2.0 → Both equally affected.
Final Answer
Both decrease by the same amount when the highest value is removed
Question 3MediumMultiple Choice
A data set is: 8,10,12,14,16. The mean is 12 and the median is 12. The value 2 is added to the data set. Which measure of center is MORE affected by adding 2?
Correct answer: D. The mean, because it drops from 12 to about 10.3
This explanation shows one way to solve the problem.
New mean (after adding 2): 8+10+12+14+16+2=62 → 62÷6≈10.3 (dropped from 12).
New median: Sorted: 2,8,10,12,14,16 → 210+12=11 (dropped from 12).
Compare the changes: Mean dropped approximately 1.7 Median dropped 1. Mean was more affected.
Final Answer
The mean, because it drops from 12 to about 10.3
Question 4HardEquation Editor
A player has scored 110,125, and 105 points in three games. The player wants an overall mean score of 115 after a fourth game. What score does the player need in the fourth game?
Enter the number only. Do not include units like $, %, or ft²
Correct answer: 120
This explanation shows one way to solve the problem.
Current sum: 110+125+105=340
Required total for mean of 115: 4×115=460
4th score needed: 460−340=120
Final Answer
120
Master MA.6.DP.1.6 with personalized practice
These are 4 of the 100+ questions Algebro has for this benchmark alone. Take the diagnostic, get a study plan that targets your gaps, and practice with an AI tutor that explains every step.
