2. O 7 In this problem, we explore the effect on the mean, median, and mode of a

Question

2. O 7 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. (Enter your answers to one decimal place.) mode 2 median3 mean (b) Add 2 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? O Adding the same constant c to each data value results in the mode, median, and mean O Adding the same constant c to each data valu O Adding the same constant c to each data value results in the mode, median, and mean decreasing by c units O Tere is no distinct pattern when the same constant is added to each data value in a set. ue results in the mode, median, and mean remaining the same.

Explanation / Answer

a) The data values are 2,2,3,6,10

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

Median = value of (5+1/2)th observation = value of 3rd observation = 3

mode =2 ( since the value 2 is repeated more no. of times.)

Mean =4.6

Median= 3

Mode=2

b) If we add 2 to each values in data set

the new values of data sets are

4,4,5,8,12

Mean = (4+4+5+8+12)/5 = 33/5=6.6

Median =  value of (5+1/2)th observation = value of 3rd observation = 5

mode =4( since the value 4 is repeated more no. of times.)

Mean =6.6

Median= 5

Mode=5

c) from part a and b we see that if we add 2 to each data values the mean, median and mode increased by 2.

Correct Answer : adding the same constant c to each data value results in mode median and mode increased by c units.

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