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 402 ​$4 comma 819 ​$8 comma 969 ​$6 comma 275 ​$4 comma 326

Answer 1

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.

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