Question

The following is the frequency distribution for the speeds in miles per hour (mph) of a sample of 35 automobiles traveling on an interstate highway. The mean speed is: ________

Speed (mph) Cumulative Frequency
50-54 2
55-59 6
60-64 11
65-69 21
70-74 30
75-79 35

Answer 1

The answer is "70.38".

Explanation:

Given:

`Speed\ \ (mph) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Cumulative \ \ Frequency\\\\50-54\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2\\\\55-59\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 6\\\\60-64\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 11\\\\65-69\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 21\\\\70-74 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 30\\\\75-79 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 35\\\\`

solution:

`Interval \ \ \ \ \ \ \ X\ \ \ \ \ \ \ F \ \ \ \ \ \ \ fX\\\\`

`50-54 \ \ \ \ \ \ \ 52 \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ \ \ 104 \\\\55-59 \ \ \ \ \ \ \ 57 \ \ \ \ \ \ \ 6\ \ \ \ \ \ \ \ \ 342 \\\\60-64 \ \ \ \ \ \ \ 62 \ \ \ \ \ \ \ 11 \ \ \ \ \ \ \ \ 682 \\\\65-69\ \ \ \ \ \ \ 67 \ \ \ \ \ \ \ 21\ \ \ \ \ \ \ 1407 \\\\70-74\ \ \ \ \ \ \ 72 \ \ \ \ \ \ \ 30 \ \ \ \ \ \ \ 2160\\\\75-79 \ \ \ \ \ \ \ 77 \ \ \ \ \ \ \ 35\ \ \ \ \ \ \ 2695 \\\\`

Total
`105 \ \ \ \ \ \ \ 7390`

`\text{mean speed}= (fX)/(F)`

`= (7390)/(105)\\\\=70.38`