Question

The daily high temperatures in degrees Fahrenheit in Allentown, PA, for a period of 10 days are shown below. 76 80 89 96 98 100 98 91 89 82 Which statement correctly describes the data?

A the median value is 98
B the upper quartile value is 96
C the lower quartile vlue is 76
d the interquartile range is 16​

Answer 1

the only correct statement is B: the upper quartile value is 96.

Explanation:

First, let's put the temperatures in order: 76, 80, 82, 89, 89, 91, 96, 98, 98, 100.

A. To find the median, we need to find the middle value in the ordered set of data. Since there are an even number of values, we take the average of the two middle values. The two middle values are 89 and 91, so the median is (89+91)/2 = 90. Therefore, statement A is false.

B. To find the upper quartile, we need to find the value that separates the highest 25% of the data from the rest. Since there are 10 values, the upper quartile is the 7th value when the data is ordered. The 7th value is 96, so statement B is true.

C. To find the lower quartile, we need to find the value that separates the lowest 25% of the data from the rest. Since there are 10 values, the lower quartile is the 3rd value when the data is ordered. The 3rd value is 82, so statement C is false.

D. The interquartile range is the difference between the upper quartile and the lower quartile. From our previous calculations, we know that the upper quartile is 96 and the lower quartile is 82. Therefore, the interquartile range is 96-82 = 14. Statement D is false.

Therefore, the only correct statement is B: the upper quartile value is 96.