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. 7,424 4,983 8,995 6,449 4,205

Answer 1

The data in ascending order is

4205 4983 6449 7424 8995

(a)

Mean = (4205 + 4983 + 6449 + 7424 + 8995) / 5 = 6411.2

(b)

Median is the middlemost element. For 5 observations, the middlemost element is (5 + 1)/2 = 3rd element.

Median = 6449

(c)

There are no values for which frequency is more than 1. Thus, the mode does not exist for the data.

(d)

Midrange = (min + max) /2

= (4205 + 8995) /2

= 6600

Median - Mean = 6449 - 6411.2 = 37.8

Midrange - Mean = 6600 - 6411.2 = 188.8

We see that there are not much large difference between mean, median and midrange. Thus, the different measures of center does not differ very​ much.