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[tex]=221+ 645+ 538+ 941+269+ 893+703+ 536+823+651=6220[/tex]
Number of observations (n) = 10
Mean [tex]\left ( \overline{x} \right )=[/tex] Sum of observations/Number of observations = [tex]\frac{6220}{10}=622[/tex]
Standard deviation:
[tex]S=\sqrt{\frac{\sum_{i=1}^{n}(x_i-\left ( \overline{x} \right ))^2}{n}}[/tex]
Put [tex]n = 10,\overline{x} =622[/tex]
[tex]\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[/tex]
[tex]S=\sqrt{\frac{523396}{10}}\\=\sqrt{52339.6}\\=228.78[/tex]
