Question

Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. 11,11,16,17,15,13,9,18,5,7

Answer 1

Range = 13

Population variance = 17.0

Population Standard deviation = 4.1

Step-by-step explanation:

Range is the measure of variability of set of data. It is the difference between the highest and lowest value in a set of data.

Given the data 11,11,16,17,15,13,9,18,5,7

Highest value = 18

Lowest value = 5

Range = 18-5 = 13

For the population variance, the formula below is suitable:

Population Variance = Σ(x-mean)²/N

N is total element in the data = 10

x are the individual data

Before we can get the variance and SD, we need to first calculate the mean

mean = Σfx/N

Mean = 122/10

Mean = 12.2

Variance = 170.16/10

Population variance = 17.016

Population variance ≈ 17.0 (to 1 d.p)

Population standard deviation = √Population Variance

Population standard deviation = √17.016 = 4.125

≈ 4.1 (to 1 d.p)

Check the attachment for the table