Question

A study conducted by the Toledo police at the intersection of Byrne and Heatherdowns for the 7 to 9 AM drive time revealed the follwoing number of vehicles that proceeded through the intersection after the light changed. The information reported is for a SAMPLE of 6 days during a 1 month period.6 12 7 12 8 9Find the mean, median, mode and standard deviation for the SAMPLE.

Answer 1

(a)Mean=9

(b)Median=9.5

(c)Mode=12

(d)Standard Deviation=2.53

Explanation:

The sample of the number of vehicles that proceeded through the intersection after the light changed for 6 days during a 1 month period is given below:

6 12 7 12 8 9

(a)Mean

`Mean=(6+12+ 7+ 12+ 8+ 9)/(6) \\=(54)/(6) \\Mean=9`

(b)Median

First, arrange in ascending order

6,7,8,9,12,12

Since we have two terms in the middle, we take the average.

`Median=(8+9)/(2)\\Median=8.5`

(c)Mode

The mode is the number with the highest frequency. The mode number of cars is 12.

(d)Standard Deviation

`S.D.=\sqrt{\frac{\sum_(i=1)^(n)(x-\bar{x})^2}{n-1}}`

`S.D.=\sqrt((6-9)^2+(7-9)^2+(8-9)^2+(9-9)^2+(12-9)^2+(12-9)^2)/(6-1)`

`=√(6.4) \\S.D.=2.53`