Question

Which choice below is most likely the value of the mean of the data set shown in the histogram above?

Answer 1

9.86

Explanation:

To estimate the mean from the histogram, first, find the total frequency.

`\text{Total Frequency}=8+4+7+1+6+2=28`

Next, calculate the midpoint of each of the bars.

`\begin{gathered} (0+4)/(2)=(4)/(2)=2 \\ (4+8)/(2)=(12)/(2)=6 \\ (8+12)/(2)=(20)/(2)=10 \\ (12+16)/(2)=(28)/(2)=14 \\ (16+20)/(2)=(36)/(2)=18 \\ (20+24)/(2)=(44)/(2)=22 \end{gathered}`

Multiply the midpoint of each bar by their respective frequencies; then find the total.

`\begin{gathered} 2*8=16 \\ 6*4=24 \\ 10*7=70 \\ 14*1=14 \\ 18*6=108 \\ 22*2=44 \\ \text{Total}=16+24+70+14+108+44=276 \end{gathered}`

Finally, divide the total obtained by the total frequency.

`\text{Mean}=(276)/(28)=9.86`

The estimated mean from the histogram is 9.86.