Question

Module 02 Homework Assignment

1. The data set below shows the ages of 10 randomly selected drivers who recently filed car insurance claims. Calculate the mean, median, mode and midrange for the data set below. Show your calculations and interpret your results in context of the problem.

51    50   47   50    48     41    59     47     45    37

Mean: Interpretation:

Median: Interpretation:

Mode: Interpretation:

Midrange: Interpretation:

2. Determine whether the statements below are true or false. If you answer false, explain why the statement is not true.

1. All of the data values in a data set are the same. The standard deviation of this data set is 0. ____________________________

2. The standard deviation is always positive. __________________

3. If the standard deviation of a data set is 4, then the variance of the data set is 16. _________________

4. If the variance of a data set is 16, then the standard deviation is 4. ________________

5. If the standard deviation of a data set is 9, then the variance is 3. ________________

Answer 1

Mean : the mean of the following observations is (37+41+45+47+47+48+50+50+51+59)/10 = 47.5

it is to be noted that near the ages of 47 years 6 months, drivers filed car insurance claims.

Median : the median is any value between 47 (5th value) and 48 (6th value).

The given data is very likely to be a symmetric , so mean median and mode are very close to each other so the conclusion about median is the same as the mean.

Mode : the given data is a bimodal data , it has two modes 47 and 50 (most frequently observed)

specially at the age of 47 and 50 many drivers filed car insurance claims.

Midrange : the value of the midrange is (37+59)/2 = 48.

After determine the mean , median , mode , midrange it is clear that the given data is symmetric and drivers are prefer to file the car insurance policy at the ages around 47-50

TRUE if all the data are same , no variation is available in the data , so variance will become zero as well as standard deviation will be zero.

TRUE because it is a term having sum of squares quantity , so minimum value will be zero. so it is always positive.

TRUE because standard deviation is nothing but the square root of the variance.

FALSE the reason is given in the last answer.