Compare standard deviation of data sets (ACT). Game on.

Compare standard deviation of data sets (ACT) is a grade 9 math skill aligned to Common Core standard HSS.ID.A.2: use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 compare standard deviation of data sets (act) problems our math games drill.

CCSS HSS.ID.A.210 questions in the bank
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Warm-upeasy

Four data sets show daily high temperatures (in °F). Which set has the greatest standard deviation?

Set A: 20,22,24,2620, 22, 24, 26
Set B: 21,23,25,27,2921, 23, 25, 27, 29
Set C: 10,22,24,26,2810, 22, 24, 26, 28
Set D: 22,23,24,25,2622, 23, 24, 25, 26

Set C includes the outlier 1010 while the other values cluster near 2424, so values are far from the mean 2222. Its standard deviation is about 6.36.3, greater than the evenly spaced sets A, B, and D.

Mid-gameeasy

Four small data sets are listed below. Which set has the least standard deviation?

Set A: 3,7,11,153, 7, 11, 15
Set B: 6,8,10,12,146, 8, 10, 12, 14
Set C: 8,9,10,11,128, 9, 10, 11, 12
Set D: 4,8,12,16,204, 8, 12, 16, 20

Set C has mean 1010 with values within one step of the center (88 through 1212), giving the smallest standard deviation, about 1.41.4. Sets A, B, and D spread farther from their means.

Mid-gameeasy

A survey recorded the number of text messages sent per day. Which group has the greatest standard deviation?

Group A: 50,50,50,50,5050, 50, 50, 50, 50
Group B: 40,45,50,55,6040, 45, 50, 55, 60
Group C: 48,49,50,51,5248, 49, 50, 51, 52
Group D: 30,50,50,50,7030, 50, 50, 50, 70

Group D has mean 5050 with values 3030 and 7070 each 2020 away from the center while three values sit at the mean, giving a standard deviation of about 12.612.6. Groups B and C spread less; Group A has zero spread.

Mid-gameeasy

Four data sets show the number of laps run in five trials. Which set has the least standard deviation?

Set A: 2,4,6,8,102, 4, 6, 8, 10
Set B: 5,5,6,6,85, 5, 6, 6, 8
Set C: 1,5,6,7,111, 5, 6, 7, 11
Set D: 3,5,6,7,93, 5, 6, 7, 9

Set B has mean 66 with repeated values near the center (5,5,6,6,85, 5, 6, 6, 8), giving the smallest standard deviation, about 1.11.1. The other sets include values farther from their means.

Mid-gameeasy

Four small data sets are listed below. Which set has the least standard deviation?

Set A: 7,9,11,137, 9, 11, 13
Set B: 8,10,10,128, 10, 10, 12
Set C: 5,10,10,155, 10, 10, 15
Set D: 6,9,11,146, 9, 11, 14

Set B has mean 1010 with two values at the mean and the others only two units away, giving the smallest standard deviation, about 1.41.4. Sets A, C, and D spread farther from their means.

Mid-gameeasy

Four data sets show minutes spent on homework each night. Which set has the greatest standard deviation?

Set A: 18,20,22,24,2618, 20, 22, 24, 26
Set B: 19,21,23,2519, 21, 23, 25
Set C: 15,20,25,3015, 20, 25, 30
Set D: 20,21,22,23,2420, 21, 22, 23, 24

Set C has mean 22.522.5 with values stepping by 55 from 1515 to 3030, so each value is far from the center; its standard deviation is about 5.65.6. Sets A and B spread less evenly, and Set D is tightly clustered.

Mid-gameeasy

Four data sets record the number of pages read in four or five sessions. Which set has the least standard deviation?

Set A: 4,8,12,164, 8, 12, 16
Set B: 6,8,10,12,146, 8, 10, 12, 14
Set C: 7,8,9,10,117, 8, 9, 10, 11
Set D: 2,6,10,14,182, 6, 10, 14, 18

Set C has mean 99 with consecutive values from 77 to 1111, each only one or two units from the center, giving the smallest standard deviation, about 1.41.4. Sets A, B, and D spread farther from their means.

Buzzer beatermedium

Four data sets list quiz scores out of 120120. Which set has the greatest standard deviation?

Set A: 100,102,104,106100, 102, 104, 106
Set B: 80,90,100,110,12080, 90, 100, 110, 120
Set C: 98,99,100,101,10298, 99, 100, 101, 102
Set D: 90,95,100,105,11090, 95, 100, 105, 110

Set B has mean 100100 with values stepping by 1010 from 8080 to 120120, so each score is up to 2020 points from the center; its standard deviation is about 14.114.1. Set D also centers on 100100 but steps by only 55 (range 2020, not 4040), giving a smaller standard deviation of about 7.17.1. Sets A and C stay even closer to their means.

Tests that cover compare standard deviation of data sets (act):
NAEPACTPSAT 8/9VTCAPNC EOG/EOC
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