Question

Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 56.3 degrees.Low Temperature (OF) 40-44 45-49 50-54 55-59 60-64 0Frequency37 11 5 2degrees.The mean of the frequency distribution is(Round to the nearest tenth as needed.)

Answer 1

To find the mean of a frequency distribution with intervals, we first need to find the midpoint of each interval.

We do that by adding the limits of each interval and dividing by 2:

1

`(40+44)/(2)=42`

2

`(45+49)/(2)=47`

3

`(50+54)/(2)=52`

4

`(55+59)/(2)=57`

5

`(60+64)/(2)=62`

Now, we multiply these midpoints by the frequency of each interval and sum them:

`\begin{gathered} 3\cdot42+7\cdot47+11\cdot52+5\cdot57+2\cdot62 \\ 126+329+572+285+124=1436 \end{gathered}`

Now, we divide this sum by the sum of the frequencies, and this will be the mean.

`m=(1436)/(3+7+11+5+2)=(1436)/(28)=51.3`

So, the mean calculated by using the frequency distribution is 51.3, which is lower than the actual mean of the data, 56.3.