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 2, 2, 3, 6, 10. (a) Compute the mode, median, and mean. (b) Add 5 to each of the data values. 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 the same constant is added to each data value in a set?

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danielafalvarenga danielafalvarenga · Answer 1 · 2019-09-15T15:08:05+02:00

Answer:

a) Mode: 2 Median: 3 Mean: 4.6

b) Mode: 7 Median: 8 Mean: 9.6

c) Just added 5 to values. General below.

Step-by-step explanation: 2, 2, 3, 6, 10

a) Mode: 2 (Most apperances)

Median: 3 (odd data, middle number)

Mean: (2+2+3+6+10)/5 = 23/5 = 4.6

b) + 5

Data: 7,7,8,11,15

Mode: 7 (Most apperances)

Median: 8 (odd data, middle number)

Mean: (7+7+8+11+15)/5 = 48/5 = 9.6

c) The results from (b) is (a) + 5

In general: Let's add x to the same data provided:

2+x, 2+x, 3+x, 6+x, 10+x,

For the mode, it does not matter, the number with most apperances will continue to be the mode + x

For the median, same thing. It is just the median + x

For the mean, same thing. For the set of 5 numbers:

(2+x + 2+x + 3+x + 6+x + 10+x)/5 =

(23+5x)/5

23/5 + 5x/5 =

23/5 + x

For example, If it was 6 numbers, we would add 6 times that number and divide it by 6, adding x to the mean.