Consider the data set below

Asked by maham237 @ 06/01/2021 in Mathematics viewed by 321 People

Consider the data set. 2, 5, 6, 7, 9 (a) Find the range. 7 Correct: Your answer is correct. (b) Use the defining formula to compute the sample standard deviation s. (Round your answer to two decimal places.) 2.7 Incorrect: Your answer is incorrect. (c) Use the defining formula to compute the population standard deviation σ. (Round your answer to two decimal places.) -6.23 Incorrect: Your answer is incorrect.

Answered by maham237 @ 06/01/2021

Answer:

A) 7

B) 2.588

C) 2.3151

Step-by-step explanation:

We are given the following data set:

2, 5, 6, 7, 9

Formula:

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

Mean = $\displaystyle\frac{29}{5} = 5.8$

a) Range

= Highest value - Lowest Value = 9 - 2 = 7

b) Sample standard deviation

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

Sum of squares = 14.44 + 0.64 + 0.04 + 1.44 + 10.24 = 26.8

$SS.D = \sqrt{\frac{26.8}{4}} = 2.588$

c) Population standard deviation

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

Sum of squares = 14.44 + 0.64 + 0.04 + 1.44 + 10.24 = 26.8

$PS.D = \sqrt{\frac{26.8}{5}} = 2.3151$

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