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

Answer:

Mean = 8

Mode = 12

Median = 7.5

Standard deviation = 3.07

Step-by-step 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.  

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

$Mean =\displaystyle\frac{64}{8} = 8$

Sum of squares of differences = 66

$S.D = \sqrt{\dfrac{66}{7}} = 3.07$

Mode is the most frequent observation of data.

Mode = 12

Since it repeats two times.

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$

Sorted data:  4, 5, 6, 7, 8, 10, 12, 12

$\text{Median} = \dfrac{4^{th}+5^{th}}{2} = \dfrac{7+8}{2}=7.5$