Question

An insurance institute conducted tests with crashes of new cars traveling at 6​ mi/h. The total cost of the damages was found for a simple random sample of the tested cars and listed below. Find the​ (a) mean,​ (b) median,​ (c) mode, and​ (d) midrange for the given sample data. Do the different measures of center differ very​ much? ​$7 comma 542 ​$4 comma 853 ​$8 comma 989 ​$6 comma 294 ​$4 comma 215

Answer 1

a) Mean = $ 6378.6

b) Median = $ 6,294

c) No mode

d) Midrange = $ 6602

Explanation:

Given data;

observations :

​$7,542

​$4,853

​$8,989

​$6,294

​$4,215

total number of observations = 5

Now

a) Mean = (Sum of all the observations) / (Total number of observations )

or

Mean = ($7,542 + ​$4,853 + ​$8,989 + $6,294 + ​$4,215) / 5

or

Mean = $ 31893 / 5

or

Mean = $ 6378.6

b) Median

for median, arrange the data in the ascending order, we have

$4,215 , ​$4,853 , ​$6,294 , ​$7,542 , ​$8,989

the median of the 5 observations is the 3rd observation

hence, median = $ 6,294

c) Mode

mode is the highest occurring observation

here every observation is unique thus no mode

d) Midrange of the given observation

Midrange = (Highest value + lowest value) / 2

or

Midrange = ( $4,215 + ​$8,989 ) / 2

or

Midrange = 13204 / 2

or

Midrange = $ 6602

Yes, the different measure of the center differs much