Question

listed below are the amounts of time (in months) that the employees of a restaurant have been working at the restaurant. find the mean for the given sample data. 1 5 6 8 11 14 17 46 61 90 99 126 143 167 round your answer to one more decimal place than the original data values. a. 52.9 months b. 31.5 months c. 56.7 months d. 61.1 months

Explanation:

Step1: Count the number of data points

The data set is: 1, 5, 6, 8, 11, 14, 17, 46, 61, 90, 99, 126, 143, 167. Let's count the number of values, \( n \).
Counting them, we have \( n = 14 \).

Step2: Sum all the data points

Now, we calculate the sum \( \sum x \) of all the values:
\[

$$\begin{align*} 1 + 5 + 6 + 8 + 11 + 14 + 17 + 46 + 61 + 90 + 99 + 126 + 143 + 167&=(1 + 5)+(6 + 8)+(11 + 14)+(17 + 46)+(61 + 90)+(99 + 126)+(143 + 167)\\ &=6 + 14 + 25 + 63 + 151 + 225 + 310\\ &=(6 + 14)+(25 + 63)+(151 + 225)+310\\ &=20 + 88 + 376 + 310\\ &=(20 + 88)+(376 + 310)\\ &=108 + 686\\ &=794 \end{align*}$$

\]

Step3: Calculate the mean

The formula for the mean \( \bar{x} \) of a sample is \( \bar{x}=\frac{\sum x}{n} \).
Substituting \( \sum x = 794 \) and \( n = 14 \) into the formula:
\[
\bar{x}=\frac{794}{14}\approx56.714\approx56.7
\]

Answer:

C. 56.7 months