In this problem, we explore the effect on the mean, median, and mode of multiply

Question

In this problem, we explore the effect on the mean, median, and mode of multiplying each data value by the same number. Consider the following data set. 5, 5, 6, 9, 13

(a) Compute the mode,

median,

and mean.

mode

(b) Multiply each data value by 4.

Compute

the mode,

median,

and mean.

(c) Compare the results of parts (a) and (b). In general, how do you think the mode, median, and mean are affected when each data value in a set is multiplied by the same constant?

Multiplying each data value by the same constant c results in the mode, median, and mean increasing by a factor of c. Multiplying each data value by the same constant c results in the mode, median, and mean remaining the same.

Multiplying each data value by the same constant c results in the mode, median, and mean decreasing by a factor of c.

There is no distinct pattern when each data value is multiplied by the same constant.

(d) Suppose you have information about average heights of a random sample of airline passengers. The mode is 68 inches, the median is 70 inches, and the mean is 65 inches. To convert the data into centimeters, multiply each data value by 2.54.

What are the values of the mode, median, and mean in centimeters? (Enter your answers to two decimal places.)

mode cm

median cm

mean cm

Explanation / Answer

A) 5, 5, 6, 9, 13

Mean = Sum of all observations/ Total no. of Observations

= (5+5+6+9+13) / 5

= 7.6

Median = 6 ( The middle most observation when arranged increasing/decreasing order )

Mode = 5 ( The most frequently occuring observation)

B)  20, 20, 24, 36, 52

Mean = (20+20+24+36+52) / 5

=  7.6 * 4

= 30.4

Median = 24 = 6 *4 ( The middle most observation when arranged increasing/decreasing order )

Mode = 20 = 5*4 ( The most frequently occuring observation)

c) From the observations

Multiplying each data value by the same constant c results in the mode, median, and mean increasing by a factor of c.

d)

mode=68 inches = 68 x 2.54 = 172.7cm

median = 70 inches = 70 x 2.54 = 177.8 cm

mean = 65 inches. = 65 x 2.54 =  165.1 cm

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