Question

A study conducted by the Toledo police at the main intersection of the city between 7 to 9 AM revealed the number of vehicles proceeded through the intersection after light changed. Here is the information of 8 days during the study period:

Number of vehicle: 6, 12, 7, 8, 4, 5, 12, 10.

Find the mean, median, mode and standard deviation for the SAMPLE.

Answer 1

Mean = 8

Mode = 12

Median = 7.5

Standard deviation = 3.07

Explanation:

We are given the following sample in the question:

6, 12, 7, 8, 4, 5, 12, 10

Formula:

`\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}`

where
`x_i` are data points,
`\bar{x}` is the mean and n is the number of observations.

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

`Mean =\displaystyle(64)/(8) = 8`

Sum of squares of differences = 66

`S.D = \sqrt{(66)/(7)} = 3.07`

Mode is the most frequent observation of data.

Mode = 12

Since it repeats two times.

`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: 4, 5, 6, 7, 8, 10, 12, 12

`\text{Median} = (4^(th)+5^(th))/(2) = (7+8)/(2)=7.5`