The tables below give the distribution of high temperatures in degrees Fahrenheit (°F) for City A and City B over the same 21 days in March. City A Temperature(°F) Frequency 80 3 79 14 78 2 77 1 76 1 City B Temperature(°F) Frequency 80 6 79 3 78 2 77 4 76 6 Which of the following is true about the data shown for these 21 days?

Correct Answer is : The standard deviation of temperatures in City A is larger.

The standard deviation of temperatures in City A is larger.

The standard deviation of temperatures in City A is the same as that of City B.

The standard deviation of temperatures in these cities cannot be calculated with the data provided.

SAT Mathematics Practice Test 4

Question : 43 of 58

Marks: +1, -0

The tables below give the distribution of high temperatures in degrees Fahrenheit (°F) for City A and City B over the same 21 days in March.
City A

Temperature(°F)	Frequency
80	3
79	14
78	2
77	1
76	1

City B

Temperature(°F)	Frequency
80	6
79	3
78	2
77	4
76	6

Which of the following is true about the data shown for these 21 days?

The standard deviation of temperatures in City A is larger.
The standard deviation of temperatures in City A is larger.
The standard deviation of temperatures in City A is the same as that of City B.
The standard deviation of temperatures in these cities cannot be calculated with the data provided.

Validate

Solution:

The standard deviation is a measure of how far the data set values are from the mean. In the data set for City A, the large majority of the data are in three of the five possible values, which are the three values closest to the mean. In the data set for City B, the data are more spreadout, with many values at the minimum and maximum values. Therefore, by observation, the data for City B have a larger standard deviation.
Alternatively, one can calculate the mean and visually inspect the difference between the data values and the mean. For City A the mean is

{1,655}/21≈78.8

and for City B the mean is

{1.637}/21≈78.0

The data for City A are closely clustered near 79, which indicates a small standard deviation. The data for City B are spread out away from 78, which indicates a larger standard deviation.
Choices A, C, and D are incorrect and may be the result of misconceptions about the standard deviation.

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