Answer:
Option A) 4.4 is the correct standard deviation of the the given data set.
Step-by-step explanation:
We are given the following data set:
127, 135, 128, 131, 133, 127, 122
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
Solving:
[tex]Mean =\displaystyle\frac{903}{7} = 129[/tex]
Sum of squares of differences = 4 + 36 + 1 + 4 + 16 + 4 + 49 = 114
[tex]S.D = \sqrt{\frac{114}{6}} = 4.358898944 \approx 4.4[/tex]
Option A) is the correct standard deviation of the the given data set.
