Question

The number of cars sold at a dealership over several weeks is given below. 14, 23, 31, 29, 33 What is the standard deviation for this set of population data?

Answer 1

The answer is A.6.9.............................

Answer 2

Hence, standard deviation is: 6.87

Explanation:

We are given the data as:

14 23 31 29 33

The mean of the data is calculated as the ratio of the sum of all the data points divided by the total number of data points.

Hence,

`Mean(M)=(14+23+31+29+33)/(5)\\\\Mean(M)=(130)/(5)\\\\Mean(M)=26`

Now we find the difference between mean and each data entry.

14-26 23-26 31-26 29-26 33-26

-12 -3 5 3 7

Now squaring these numbers to get:

144 9 25 9 49

Now, finding the mean we get the variance(V) as:

`V=(144+9+25+9+49)/(5)\\\\\\V=(236)/(5)\\\\\\V=47.2`

Now, standard deviation is defined as the square root of the variance.

Hence standard deviation is:

`√(47.2)=6.87`

Hence, standard deviation is: 6.87