Question

11. Calculate the sample standard deviation of the number of letters for the ten words in your sample. Round your answer to three decimal places.

Answer 1

sample standard deviation of 10 letter counts (9,6,8,9,6,7,5,5,6,7) is 1.476

Explanation:

Sample standard deviation is the square root of the equation (sample varaince)

That is, sum of the square differences from the mean divided by (sample size -1) : Σ (
`(((x_(i) - M)^2)/(n-1) )` where

• x_{i} is the number of the letters for the ith word in the sample

• M is the mean number of letters in the sample

• n is the sample size.

Lets create 10 word and their letter counts sample using some of the words of the question:

{Calculate : 9, sample: 6, standard: 8, deviation: 9, number: 6, letters: 7, words: 5, Round: 5, answer: 6, decimal: 7}

The elements of the sample are:

9,6,8,9,6,7,5,5,6,7

Mean of the sample is: (
`M=(9+6+8+9+6+7+5+5+6+7)/(10) =6.8`)

Sample variance is:

`((9-6.8)^(2)+(6-6.8)^(2)+(8-6.8)^(2)+(9-6.8)^(2)+(6-6.8)^(2)+(7-6.8)^(2)+(5-6.8)^(2)+(5-6.8)^(2)+(6-6.8)^(2)+(7-6.8)^(2) )/(10-1)`≈2.178

And finally sample standard deviation is :
`√(2.178)` ≈1.476