Question

13. Listed below are the amounts of time (in months) that the employees of a restaurant have been working at the restaurant. Find the standard deviation of the data set, rounding to one more decimal place than is present in the data. 2 3 5 13 22 35 60 86 101 122


a. 44.5 months

b.42.2 months

c. 45.8 months

d. 43.3 months

Answer 1

Answer:

Option B) 42.2 months

Step-by-step explanation:

We are given the following data of the amount of time in months.

2, 3, 5, 13, 22, 35, 60, 86, 101, 122

We have to find the standard deviation.

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}$  

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.  

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{449}{10} = 44.9$

Sum of squares of differences =

1840.41 + 1755.61 + 1592.01 + 1017.61 + 524.41 + 98.01 + 228.01 + 1689.21 + 3147.21+ 5944.41 = 17836.9

$\sigma = \sqrt{\dfrac{17836.9}{19}} = 42.2$

Thus, the standard deviation of given data set is 42.2 months.

Option B) 42.2 months