Grade 6 · Statistics & probability

Mean change from data set edits practice

Mean change from data set edits is a grade 6 math skill aligned to Common Core standard 6.SP.B.5: summarize numerical data sets in relation to their context, reporting measures of center and variability. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 mean change from data set edits problems our math games drill.

CCSS 6.SP.B.510 questions in the bank
Sample questions

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Question 1easy

A weather station records five daily rainfall amounts, in inches: 11, 22, 33, 44, and 55. The lowest amount, 11 inch, is removed from the data set. How does this affect the mean?

The mean of the original five amounts is 1+2+3+4+55=3\dfrac{1+2+3+4+5}{5}=3 inches. Because 1<31<3, removing the smallest value raises the mean.

Question 2easy

A runner logs five lap times, in seconds: 1818, 2020, 2222, 2424, and 2626. A sixth lap time of 1616 seconds is added to the data set. How does this affect the mean?

The mean of the original five times is 18+20+22+24+265=22\dfrac{18+20+22+24+26}{5}=22 seconds. Because 16<2216<22, adding 1616 pulls the mean down.

Question 3easy

A biologist measures five plant heights, in inches: 5858, 6060, 6262, 6464, and 6666. The tallest plant, 6666 inches, is removed from the data set. How does this affect the mean?

The mean of the original five heights is 58+60+62+64+665=62\dfrac{58+60+62+64+66}{5}=62 inches. Because 66>6266>62, removing the largest value lowers the mean.

Question 4easy

A bookstore tracks five daily sales totals, in dollars: 1010, 1515, 2020, 2525, and 3030. A sixth day with sales of 2020 is added to the data set. How does this affect the mean?

The mean of the original five totals is 10+15+20+25+305=20\dfrac{10+15+20+25+30}{5}=20 dollars. Because the new value equals the current mean, the mean stays 2020.

Question 5easy

A student logs five daily page counts: 2020, 2525, 3030, 3535, and 4040. A sixth day with 4545 pages read is added to the data set. How does this affect the mean?

The mean of the original five counts is 20+25+30+35+405=30\dfrac{20+25+30+35+40}{5}=30 pages. Because 45>3045>30, adding 4545 pulls the mean up.

Question 6easy

A shipping clerk weighs five packages at 5050, 5555, 6060, 6565, and 7070 pounds. The 7070-pound package is removed from the data set. How does this affect the mean?

The mean of the original five weights is 50+55+60+65+705=60\dfrac{50+55+60+65+70}{5}=60 pounds. Because 70>6070>60, removing the heaviest package lowers the mean.

Question 7medium

A cyclist records five ride distances, in miles: 1212, 1515, 1818, 2121, and 2424. Another ride distance is added to the data set, but its length is not given. How does this affect the mean?

The mean of the five known distances can be found, but the effect of the change depends on the unknown sixth distance. Without that value, the new mean cannot be determined.

Question 8medium

Five test scores are 7070, 7878, 8484, 9090, and 9696. One score is removed from the data set, but which score was removed is not stated. How does this affect the mean?

The mean of the five given scores can be found, but removing a different score changes the mean in different ways. Without knowing which score was removed, the effect cannot be determined.

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