Question

The lifetimes of a group of 10 light bulbs are given below: 221, 645, 538, 941, 269, 893, 703, 536, 823, 651. The standard deviation of the lifetimes is (to two decimal places)

Answer 1

Answer:

228.78

Step-by-step explanation:

Given:

The lifetimes of a group of 10 light bulbs are 221, 645, 538, 941, 269, 893, 703, 536, 823, 651.

To find: standard deviation of the lifetimes

Solution:

Sum of observations$=221+ 645+ 538+ 941+269+ 893+703+ 536+823+651=6220$

Number of observations (n) = 10

Mean $\left ( \overline{x} \right )=$ Sum of observations/Number of observations = $\frac{6220}{10}=622$

Standard deviation:

$S=\sqrt{\frac{\sum_{i=1}^{n}(x_i-\left ( \overline{x} \right ))^2}{n}}$

Put $n = 10,\overline{x} =622$

$\sum_{i=1}^{10}(x_i-\overline{x} )^2=(221-622)^2+(645-622)^2+(538-622)^2+(941-622)^2+(269-622)^2+(893-622)^2+(703-622)^2+(536-622)^2+(823-622)^2+(651-622)^2=523396$

$S=\sqrt{\frac{523396}{10}}\\=\sqrt{52339.6}\\=228.78$