Math  /  Data & Statistics

QuestionYour friend finds the mean and median of the data set: 40,38,62,70,56,41,58,48,6040,38,62,70,56,41,58,48,60, 45. Your friend says that the mean and median are both 52 . Is your friend correct? If not, find the correct answer. (1 point) My friend is correct. My friend is not correct. The mean is 51.8 . The median is 48.5 . My friend is not correct. The mean is 51.8 . The median is 52 . My friend is not correct. The mean is 52. The median is 51.8 .

Studdy Solution

STEP 1

1. The data set contains ten data points: 40,38,62,70,56,41,58,48,60,45 40, 38, 62, 70, 56, 41, 58, 48, 60, 45 .
2. The mean is the sum of all data points divided by the number of data points.
3. The median of a set with an even number of elements is the average of the two middle values.

STEP 2

1. Calculate the mean of the data set.
2. Order the data points and determine the median.

STEP 3

Calculate the sum of all data points:
40+38+62+70+56+41+58+48+60+45=518 40 + 38 + 62 + 70 + 56 + 41 + 58 + 48 + 60 + 45 = 518

STEP 4

Divide the sum by the number of data points (10) to find the mean:
51810=51.8 \frac{518}{10} = 51.8

STEP 5

Order the data points:
38,40,41,45,48,56,58,60,62,70 38, 40, 41, 45, 48, 56, 58, 60, 62, 70

STEP 6

Since there are 10 data points, the median is the average of the 5th and 6th values:
48+562=1042=52 \frac{48 + 56}{2} = \frac{104}{2} = 52
The mean is 51.8 51.8 and the median is 52 52 .
My friend is not correct. The mean is 51.8. The median is 52.

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