AnswersIntegrated Math II FullComparing Measures of Center and Variability

Comparing Measures of Center and Variability Answers

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The means and mean absolute deviations of the individual times of members on two relay track teams are shown in the table below.Means and Mean Absolute Deviations of Individual Times of Members of Relay Track Teams Team ATeam BMean59.32 s59.1 sMean Absolute Deviation1.5 s2.4 sWhat is the ratio of the difference in the means of the two teams to the mean absolute deviation of Team B?

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A
0.09
B
0.15
C
0.25
D
0.65
2
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Last week’s and this week’s low temperatures are shown in the table below.Low Temperatures for 5 Days This Week and Last WeekLow TemperaturesThis Week ()410696Low TemperaturesLast Week ()139585Which measures of center or variability are greater than 5 degrees? Select three choices.

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A
the mean of this week’s temperatures
B
the mean of last week’s temperatures
C
the range of this week’s temperatures
D
the mean absolute deviation of this week’s temperatures
E
the mean absolute deviation of last week’s temperatures
3

Tyrell recorded his science scores and his math scores. The measures of center and variation for each score are shown in the table below.Measures of Center and Variationfor Tyrell’s Science and Math Scores ScienceMathMean7880Median8080Mode6085Range4015Mean Absolute Deviation14.44.0Which inference can be made when analyzing the data in the table?

A
There is more variation in the science scores.
B
Tyrell prefers math over science.
C
The mode is the best measure of the typical score for both science and math.
D
The median for each subject is the same as the mean.
4

The heights, in feet, of the trees for sale at two nurseries are shown below.Yard Works: 7, 9, 7, 12, 5The Grow Station: 9, 11, 6, 12, 7Which statements are true regarding the measures of center and variability of these data sets? Select three choices.

A
The mean of the tree heights at Yard Works is less than the mean of the tree heights at The Grow Station.
B
The median of the tree heights at Yard Works is greater than the median of the tree heights at The Grow Station.
C
The range of the tree heights at Yard Works is greater than the range of the tree heights at The Grow Station.
D
The mean absolute deviation of the tree heights at Yard Works is greater than the mean absolute deviation of the tree heights at The Grow Station.
E
The mean absolute deviation of the tree heights at Yard Works is equal to the mean absolute deviation of the tree heights at The Grow Station.
5

The means and mean absolute deviations of the amount of rain that fell each day in a local city, last week and this week, are shown below.Means and Mean Absolute Deviations of Rainfall Last Week and This Week Last WeekThis WeekMean 19.7 cm19.3 cmMean Absolute Deviation4.6 cm5.2 cmThe difference in the mean rainfall is approximately what percent of the mean absolute deviation of the this week’s rainfall?

A
8%
B
23%
C
27%
D
67%
6

The means and mean absolute deviations of the individual times of members of two relay swim teams are shown in the table below.Means and Mean Absolute Deviations of Individual Times of Members of Relay Swim Teams Team ATeam BMean127.9 s127.4 sMean Absolute Deviation0.26 s0.23 sThe difference of the means is found and then compared to each of the mean absolute deviations. Which is true?

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A
The difference between the mean times is about equal to the mean absolute deviation of the data sets.
B
The difference between the mean times is about 2 times the mean absolute deviation of the data sets.
C
The difference between the mean times is about 5 times the mean absolute deviation of the data sets.
D
The difference between the mean times is about 16 times the mean absolute deviation of the data sets.
7

Georgina likes to read during her summer break. The table below shows the number of pages in each book she read last summer and the number of pages in each book she read this summer.Number of Pages Georgina Reads during the SummerLast Summer140220190180190This Summer150170150190180What inference can someone draw about the data?

A
The books she read this summer had more pages, on average, than last summer.
B
The number of pages in each book varied more last summer than this summer.
C
Last summer, the average book had nearly twice the number of pages than the average book has this summer.
D
This summer, the number of pages in a book varied nearly twice as much as the number of pages in last summer's books
8

Theo recorded the means and mean absolute deviations of his language arts and Biology scores. He found the difference in the means of the scores of the two subjects. What is the approximate ratio of the difference in the means to each of the mean absolute deviations?Means and Mean Absolute Deviations of Theo’s Scores Language ArtsBiologyMean9890Mean Absolute Deviation3.55

A
2
B
5
C
18
D
28
9

Joaquin and Trisha are playing a game in which the lower median wins the game. Their scores are shown below.Joaquin’s scores: 75, 72, 85, 62, 58, 91Trisha’s scores: 92, 90, 55, 76, 91, 74Which supports the conclusion that Joaquin won the game?

A
Joaquin won because the median of his scores is 73.5 and the median of Trisha’s scores is 83.
B
Joaquin won because the median of his scores is 83 and the median of Trisha’s scores is 73.5.
C
Trisha won because the median of her scores is 73.5 and the median of Joaquin’s scores is 83.
D
Trisha won because the median of her scores is 83 and the median of Joaquin’s scores is 73.5.
10

Enzo and Zahra are playing a game. Their scores for five games are shown in the table below.Enzo’s and Zahra’s ScoresEnzo’s Scores3947465038Zahra’s Scores3733453045Enzo’s mean score is 44. Zahra’s mean score is 38. How much greater is the mean absolute deviation for Zahra's scores than for Enzo's scores?

A
1.2
B
4.4
C
5.6
D
6.0

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