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 454 ​$4 comma 840 ​$8 comma 977 ​$6 comma 293 ​$4 comma 253 a. the mean is ​$ nothing. ​(type an integer or a​ decimal.) b. the median is ​$ nothing. ​(type an integer or a​ decimal.) c. select the correct choice below and fill in any answer boxes in your choice. a. the mode is ​$ nothing. ​(use a comma to separate answers as​ needed.) b. there is no mode. d. the midrange is ​$ nothing. ​(type an integer or a​ decimal.) do the different measures of center differ very​ much? a. there is a very large difference between the three measures. b. only the mean is different by a large amount. c. the median and mean differ by a very large amount. d. the different measures of center do not differ by very large amounts.

Answers

a. Mean = $6,358.2

b. median = $6,275

c. Mode = none

d. Midrange = $6,647.5

There is no much difference in the measures of center.

Step-by-step explanation:

==>Given:

​$7,402, ​$4,819, $8,969, ​$6,275, ​$4,326

==>Required:

a. Mean: sum of all values in the given sample data ÷ number of values in the sample

Mean = ​($7,402 + ​$4,819 + $8,969 + $6,275 + $4,326) ÷ 5

= $31,791 ÷ 5

Mean = $6,358.2

b. Median: this is the meddle value if the data set when ordered. Ordering the data set, we have:

$4,326, $4819, [$6,275], $7402, ​$8,969

Our median is $6,275.

c. Mode is the most common value in the data set. Therefore, we have no mode since there is no value in our data set that appears the most.

d. Mid-range = (highest value + lowest value) ÷ 2

= ($8,969 + $4,326) ÷ 2

= 13,295 ÷ 2 = $6,647.5

a) Mean = $ 6378.6

b) Median = $ 6,294

c) No mode

d) Midrange = $ 6602

Step-by-step 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



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