During a science experiment, a student measured the temperature changes of a liquid in deg… — ACT

During a science experiment, a student measured the temperature changes of a liquid in degrees Celsius at seven different intervals. The recorded changes were $15^\circ\text{C}$ , $6^\circ\text{C}$ , $20^\circ\text{C}$ , $24^\circ\text{C}$ , $7^\circ\text{C}$ , $4^\circ\text{C}$ , and $8^\circ\text{C}$ . What is the positive difference between the median and the mean of these seven recorded temperatures?

4Answer
B
6
C
8
D
12
E
16

Answer

To find the correct positive difference, we first find the mean by dividing the sum of the temperatures by 7:

(15 + 6 + 20 + 24 + 7 + 4 + 8) / 7 = 84 / 7 = 12

. We then sort the temperatures in ascending order:

4, 6, 7, 8, 15, 20, 24

. The median is the middle value of this sorted list, which is 8. The positive difference between the median and the mean is

|8 - 12| = 4

Step-by-Step Solution

Calculate the mean of the temperatures.

Mean = 12

Sum the seven values (

15 + 6 + 20 + 24 + 7 + 4 + 8 = 84

) and divide by the total number of data points (7) to get

84 / 7 = 12

Find the median of the temperatures.

Median = 8

Sort the values in ascending order:

4, 6, 7, 8, 15, 20, 24

. Since there are 7 data points, the median is the fourth value, which is 8.

Calculate the positive difference between the median and the mean.

Positive difference = 4

Subtract the median from the mean (or vice versa) and take the absolute value:

|8 - 12| = 4

Key Concept

Calculating and comparing the mean and median of a dataset, including the necessity of sorting data before finding the median.

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