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2 votes
Calculate the standard deviation of the data set below.

(7, 9, 10, 11, 13)
The standard deviation is 4
The standard deviation is 2.
The standard deviation is 10.

2 Answers

3 votes

Answer: 2

Explanation:

User Patrick Manser
by
8.6k points
4 votes

Option 2

ANSWER:

The Standard deviation of (7, 9, 10, 11, 13) is 2.

SOLUTION:

Given, data set is (7, 9, 10, 11, 13)

Standard deviation
\sigma=\sqrt{\frac{\Sigma(\mathrm{xi}-\mu) 2}{n}}

Where,
\mathrm{x}_{\mathrm{i}} is element of data set


\mu is mean of data set

n is total number observations.

Now, mean
\mu=\frac{\text {sum of observations}}{\text {number of observations}}


=(7+9+10+11+13)/(5)


=(50)/(5)

= 10

So, the mean of data set is 10.

Now, standard deviation
\sigma=\sqrt{((7-10) 2+(9-10) 2+(10-10) 2+(11-10) 2+(13-10) 2)/(5)}


\begin{array}{l}{\sigma=\sqrt{((-3) 2+(-1) 2+(0) 2+(1) 2+(3) 2)/(5)}} \\ {\sigma=\sqrt{(9+1+1+9)/(5)}} \\ {\sigma=\sqrt{(20)/(5)}} \\ {\sigma=2}\end{array}

So, the standard deviation is 2.

Hence, the second option is right, i.e. standard deviation is 2.

User Sukeshini
by
7.8k points

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