Question

Study Guide #9

In this problem, we explore the effect on the mean, median, and mode of adding the same number to each data value. Consider the data set 4, 4, 5, 8, 12.

(a) Compute the mode, median, and mean. (Enter your answers to one decimal place.)

mode
median
mean

(b) Add 5 to each of the data values. Compute the mode, median, and mean. (Enter your answers to one decimal place.)

mode
median
mean

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

Adding the same constant c to each data value results in the mode, median, and mean remaining the same.Adding the same constant c to each data value results in the mode, median, and mean decreasing by c units.    There is no distinct pattern when the same constant is added to each data value in a set.Adding the same constant c to each data value results in the mode, median, and mean increasing by c units.

Answer 1

Data set : 4, 4, 5, 8, 12

(a)

Mode: The most repeated observation is called as mode.

therefore, mode = 4 --------------(which repeated maximum number (2 times) of times)

Median= Value of ((n+1)/2)^th observation

Median = value of ((5+1)/2)^th observation

Median = value of 3^rd observation

Median = 5

Mean = 6.6

Therefore,

Mode = 4

Median = 5

Mean = 6.6

(b)

If we add 5 to each of the data value then the new data set is 9, 9, 10, 13, 17

Mode: The most repeated observation is called as mode.

therefore, mode = 9   --------------(which repeated maximum number (2 times) of times)

Median= Value of ((n+1)/2)^th observation

Median = value of ((5+1)/2)^th observation

Median = value of 3^rd observation

Median = 10

Mean = 11.6

Therefore,

Mode = 9

Median = 10

Mean = 11.6

(c)

If we add 5 to each data value then there is an increase in the values of mode, median, and mean by 5.

Therefore, adding the same constant c to each data value results in the mode, median, and mean increasing by c units.