Question

Sabine records the daily heights of a random sample of bamboo stalks, in inches. They are:

   20, 19, 17, 16, 18, 15, 20, 21

Consider the formulas:

A: s squared = StartFraction (x 1 minus x overbar) squared + (x 2 minus x overbar) squared + ellipsis + (x n minus x overbar) squared Over n minus 1. B: s = StartRoot StartFraction (x 1 minus x overbar) squared + (x 2 minus x overbar) squared + ellipsis + (x n minus x overbar) squared Over n minus 1 EndFraction EndRoot. C: Sigma squared = StartFraction (x 1 minus mu) Squared + (x 2 minus mu) squared + ellipsis + (x N minus mu) squared Over N EndFraction. D: Sigma = StartRoot StartFraction (x 1 minus mu) Squared + (x 2 minus mu) squared + ellipsis + (x N minus mu) squared Over N EndFraction EndRoot
Which formula should you use for variance?
Which formula should you use for standard deviation?

Answer 1

Answer:

Step-by-step explanation:

13.71

Step-by-step explanation:

Given the data as : 13 , 17, 9, 21

Finding the mean of the data;

sum of data set =13+17+9+21=60

Number of data set ,n,= 4

Mean= sum/n =60/4 =15

Finding the deviation from the mean

13-4=9

17-4=13

9-4=5

21-4=17

Squaring the deviations from mean

9²=81

13²=169

5²=25

17²=289

Adding the squares of deviations from the mean

81+169+25+289 =564

Finding n-1

4-1=3

Finding variance

564/3 =188

Finding the standard deviation

√188 = 13.71

Answer 2

Answer:

sample variance: option A

sample standard deviation: option B

Step-by-step explanation:

Given that we want to analyze a sample, then we need the sample variance formula and the sample standard deviation. The standard deviation is calculated by taking the square root of the variance. With sample $\bar{x}$, sample mean, is used, instead of $\mu$, the mean of the population.