Question

A survey of 8 adults employed full-time was taken. Here are their reported numbers of hours worked per week: 50, 53, 46, 46, 49, 43, 41, 41 (a) What is the mean of this data set? If your answer is not an integer, round your answer to one decimal place. (b) What is the median of this data set? If your answer is not an integer, round your answer to one decimal place. (c) How many modes does the data set have, and what are their values? Indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the mode(s), if applicable. zero modes one mode: two modes:

Answer 1

a) 46.1

b) 46

c) Two modes: 46, 41

Explanation:

We are given the following sample of hours per week:

50, 53, 46, 46, 49, 43, 41, 41

a) mean of this data set

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

`Mean =\displaystyle(369)/(8) = 46.1`

b) Median of data set

`Median:\\\text{If n is odd, then}\\\\Median = \displaystyle(n+1)/(2)th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle((n)/(2)th~term + ((n)/(2)+1)th~term)/(2)`

Sorted data:

41, 41, 43, 46, 46, 49, 50, 53

Median =

`=(4^(th)+5^(th))/(2) = (46+46)/(2) = 46`

The median of data is 46.

c) Mode of the data set

Mode is the most frequent observation in the data.

The mode of the data are 46 and 41 as they appeared two times.

Thus, there are two modes.