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: fomulas for the variance and standard deviation Which formula should you use for variance? Which formula should you use for standard deviation?

Answer 1

formula for standard deviation is equation A

for standard deviation you would use equation B

Answer 2

Answer:

Answer:

Data set : 15, 16, 17,18,19,20,20, 21

A=Mean of Data Set $=\frac{15+16+17+18+19+20+21}{8}\\\\=\frac{126}{8}\\\\=15.75$

D               D-A                      (D-A)²

15               -0.75                 0.5625

16               0.25                0.0625

17                 1.25                 1.5625

18                  2.25                5.0625

19                  3.25                  10.5625

20                  4.25                  18.0625

20                   4.25                 18.0625

21                     5.25                 27.5625

$\sum(D-A)^2=81.5$

Variance(V)

$=\frac{\sum(D-A)^2}{n}\\\\=\frac{\sum 81.5}{8}\\\\V=10.1875$

So, Variance (V)=10.1875

Standard deviation

$S=\sqrt{V}\\\\ S=\sqrt{10.1875}\\\\S=3.1917$

Standard Deviation = 3.20(approx)

$S=\frac{\sum(D-A)^2}{n}$

A=Mean

n=Number of observations

D=Values in Data set