SAT College

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)

Answers

Answer 1

Answer:

11.474

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.

Related Questions

Calculate the geometric mean return for the following data set:
-5% 6% -7% 4.7% 5.1%
(Negative Value should be indicated by minus sign. Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

Answers

The geometric mean return for the given data set is approximately 0.85%.

To calculate the geometric mean return for the given data set, we need to follow these steps:

Convert the percentage returns into decimal form.

To do this, we divide each return by 100:

-5% becomes -0.05

6% becomes 0.06

-7% becomes -0.07

4.7% becomes 0.047

5.1% becomes 0.051

Add 1 to each decimal return to obtain the growth factor:

-0.05 + 1 = 0.95

0.06 + 1 = 1.06

-0.07 + 1 = 0.93

0.047 + 1 = 1.047

0.051 + 1 = 1.051

Multiply all the growth factors together:

0.95 × 1.06 × 0.93 × 1.047 × 1.051

= 1.04251741

Take the nth root of the product, where n is the number of returns in the data set. In this case, n = 5:

[tex]1.04251741^{(1/5)}[/tex] ≈ 1.008488

Subtract 1 from the result and multiply by 100 to obtain the geometric mean return as a percentage:

(1.008488 - 1) × 100 ≈ 0.8488

For similar questions on geometric

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