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Consider the following population data:

38 40 15 12 24
a. Calculate range
b. calculate MAD (2 decimal places)
c. calculate population variance (2 decimal places)
d. calculate population standard deviation. (2 decimal places)

1 Answer

6 votes

Answer:

11.474

Step-by-step explanation:

a. To calculate the range, we subtract the smallest value from the largest value:

Range = largest value - smallest value

Range = 40 - 12

Range = 28

Therefore, the range is 28.

b. To calculate the MAD (Mean Absolute Deviation), we first need to find the mean of the data set:

Mean = (38 + 40 + 15 + 12 + 24) / 5

Mean = 25.8

Next, we find the absolute deviation of each value from the mean:

|38 - 25.8| = 12.2

|40 - 25.8| = 14.2

|15 - 25.8| = 10.8

|12 - 25.8| = 13.8

|24 - 25.8| = 1.8

Then, we find the average of these absolute deviations:

MAD = (12.2 + 14.2 + 10.8 + 13.8 + 1.8) / 5

MAD = 10.56 (rounded to 2 decimal places)

Therefore, the MAD is 10.56.

c. To calculate the population variance, we first need to find the mean of the data set (which we already calculated in part b):

Mean = 25.8

Next, we calculate the sum of the squared differences between each value and the mean:

(38 - 25.8)^2 = 147.24

(40 - 25.8)^2 = 206.01

(15 - 25.8)^2 = 110.88

(12 - 25.8)^2 = 189.54

(24 - 25.8)^2 = 2.56

Then, we find the average of these squared differences:

Population Variance = (147.24 + 206.01 + 110.88 + 189.54 + 2.56) / 5

Population Variance = 131.646 (rounded to 2 decimal places)

Therefore, the population variance is 131.646.

d. To calculate the population standard deviation, we take the square root of the population variance:

Population Standard Deviation = sqrt(131.646)

Population Standard Deviation = 11.474 (rounded to 2 decimal places)

Therefore, the population standard deviation is 11.474.

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