AnswersConcepts in Probability and Statistics - MA3120 B-CRStandard Deviation

Standard Deviation Answers

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1
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The graph shows a distribution of data.

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A
0.0625
B
0.25
C
0.5
D
1.5
2
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The students in Marly’s math class recorded the dimensions of their bedrooms in a frequency table.

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A
The histogram is right-skewed, so the mean is less than the median.
B
The histogram is right-skewed, so the mean is greater than the median.
C
The histogram is left-skewed, so the mean is less than the median.
D
The histogram is left-skewed, so the mean is greater than the median.
3

Raquel and Van live in two different cities. As part of a project, they each record the lowest prices for a gallon of gas at gas stations around their cities on the same day. Raquel’s data show and . Van’s data show and .Which statement is true about their gas-price data?

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A
Raquel’s data are most likely closer to $3.42 than Van’s data are to $3.78.
B
Van’s data are most likely closer to $3.42 than Raquel’s data are to $3.78.
C
Raquel’s data are most likely closer to $3.78 than Van’s data are to $3.42.
D
Van’s data are most likely closer to $3.78 than Raquel’s data are to $3.42.
4

Sixteen students each measured the weight of 25 pennies, in grams. The list shows their measurements.60, 62, 65, 59, 63, 63, 63, 62, 64, 62, 60, 61, 66, 64, 61, 65In each graph below, the mean is indicated by a solid vertical line segment while the standard deviations from the mean are indicated by dotted vertical line segments. Which graph represents the distribution of weights?

A
A graph shows the horizontal axis numbered 58 to x. The vertical axis is unnumbered. The graph shows an upward trend from 60 to 62.5 then a downward trend from 62.5 to 65.
Option A
B
A graph shows the horizontal axis numbered 52 to x. The vertical axis is unnumbered. The graph shows an upward trend from 60 to 62.5 then a downward trend from 62.5 to 70.
Option B
C
A graph shows the horizontal axis numbered 57 to x. The vertical axis is unnumbered. The graph shows an upward trend from 57 to 62.5 then a downward trend from 62.5 to 68.
Option C
D
A graph shows the horizontal axis numbered 58 to x. The vertical axis is unnumbered. The graph shows an upward trend from 61 to 62.5 then a downward trend from 62.5 to 64.
Option D
5

The graph represents the distribution of the lengths of play times, in minutes, for songs played by a radio station over one hour.

Question illustration
A
Most of the songs were between 3 minutes and 3.8 minutes long.
B
Most of the songs were 3.4 minutes long.
C
Most of the songs were less than 3.2 minutes long.
D
Most of the songs were more than 3.6 minutes long.
6

The mean shoe size of the students in a math class is 7.5. Most of the shoe sizes fall within 1 standard deviation, or between a size 6 and a size 9.

A
1.5
B
2.7
C
3.0
D
3.8
7

Which statements are true about a histogram with one-minute increments representing the data? Select three options.

A
A histogram will show that the mean time is approximately equal to the median time of 7.5 minutes.
B
The histogram will have a shape that is left-skewed.
C
The histogram will show that the mean time is greater than the median time of 7.4 minutes.
D
The shape of the histogram can be approximated with a normal curve.
E
The histogram will show that most of the data is centered between 6 minutes and 9 minutes.
8

Grace is looking at a report of her monthly cell-phone usage for the last year to determine if she needs to upgrade her plan. The list represents the approximate number of megabytes of data Grace used each month.700, 735, 680, 890, 755, 740, 670, 785, 805, 1050, 820, 750

A
65
B
75
C
100
D
130
9

Each histogram represents a set of data with a median of 29.5. Which set of data most likely has a mean that is closest to 29.5?

A
A graph shows the horizontal axis numbered 9 to 48. The vertical axis is numbered 1 to 5. The graph shows an upward trend from 1 to 33 then a downward trend from 33 to 45.
Option A
B
A graph shows the horizontal axis numbered 15 to 48. The vertical axis is numbered 1 to 5. The graph shows an upward trend from 1 to 30 then a downward trend from 30 to 45.
Option B
C
A graph shows the horizontal axis numbered 12 to 56. The vertical axis is numbered 2 to 8. The graph shows an upward trend from 1 to 32 then a downward trend from 32 to 56.
Option C
D
A graph shows the horizontal axis numbered 15 to 54. The vertical axis is numbered 1 to 5. The graph shows an upward trend from 1 to 24, a downward trend from 24 to 27, an upward trend from 27 to 30, a downward trend from 30 to 39, an upward trend from 39 to 45, a downward trend from 45 to 48, then an upward trend from 48 to 51.
Option D
10

A school creates a histogram representing the individual travel times for students riding the bus to school. The histogram is right-skewed, and the mean time is 25 minutes.

A
The median time is less than 25 minutes.
B
The median time is exactly equal to 25 minutes.
C
The median time is approximately equal to 25 minutes.
D
The median time is greater than 25 minutes.

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