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.4, 4, 5, 8, 12(a) Compute the mode, median, and mean.i. mode ii. median iii. mean (b) Multiply each data value by 6. Compute the mode, median, and mean.i. mode ii. median iii. 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 68inches, the median is 70 inches, and the mean is 70 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.)i. mode cmii. median cmiii. mean cm

Answer 1

a) Mean = 4.6, median = 3, mode =2

b) Mean = 13.8, median = 9, mode = 6

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

Explanation:

We are given the following data:

2, 2, 3, 6, 10

a) Mean, median and mode

Sorted data: 2, 2, 3, 6, 10

Mode is the most frequent observation in data.

Mode = 2

b) Multiplying data set by 3

6, 6, 9, 18, 30

Mode = 6

C) Comparison

The mean, median and mode of the new data increased by a factor of 3.

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

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