Question

Consider the following population data:________.

Answer 1

Answer:

a. 30

b. 11.04

c. 144.16

d. 12.00

Step-by-step explanation:

40 44 17 14 26

Rearrange the data

14, 17, 26, 40, 44

a. Calculate the range.

Range

Range can calculated as:

Maximum value - Minimum value

= 44 - 14

= 30

b. Calculate MAD. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

MAD

The formula for MAD( Mean Absolute Deviation) = x - Mean/5

Step 1

We find the mean

Mean = Sum of terms/ Number of terms

14 + 17 + 26 + 40 + 44/5

= 141/5

= 28.2

Step 2

Mean Absolute Deviation of the Population =

|14 - 28.2| + |17 - 28.2| + |26 - 28.2| + |40 - 28.2| + |44 - 28.2|

= 14.2 + 11.2 + 2.2 + 11.8 + 15.8/5

= 11.04

c. Calculate the population variance. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Population variance

The formula for Population variance

= (x - Mean)²/n

n = 5

Population variance = (14 - 28.2)² + (17 - 28.2)² + (26 - 28.2)² + (40 - 28.2)²+ (44 - 28.2)²/5

= 201.64 + 125.44 + 4.84 + 139.24 + 249.64/ 5

= 720.8/5

d. Calculate the population standard deviation. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Population standard deviation

Population Standard deviation formula = √ Population Variance

= √144.16

= 12.00666482

Approximately to 2 decimal places

= 12.00