Answer:
\(\sigma =3.74\)
Step-by-step explanation:
Given : 4.9, 4.9, 9.9, 9.9, 14.9
To Find: Standard deviation
Solution:
Total number of observations = 5
\(Mean = \frac{\text{Sum of all observations}}{\text{Total no. of observations}}\)
\(Mean = \frac{4.9+4.9+9.9+9.9+14.9}{5}\)
Mean = 8.9
Thus \(\bar{x}=8.9\)
Now, Formula of standard deviation =\(\sigma = \sqrt{\frac{\sum(x_i-{x})^2}{n}}\)
So, \(\sigma = \sqrt{\frac{(4.9-8.9)^2+(4.9-8.9)^2+(9.9-8.9)^2+(9.9-8.9)^2+(14.9-8.9)^2}{5}}\)
\(\sigma =3.74\)
Thus Option A is correct.
Hence the standard deviation of the data set is 3.74.
