Consider a data set with at least three data values. Suppose the highest value is increased by 10 and the lowest is decreased by 10. For each of the following, explain by example or use about 2 or 3 sentences. a. Does the mean change? Explain. b. Does the median change? Explain. c. Is it possible for the mode to change? Explain.

a. Mean doesn't change.

b. Median doesn't change.

c. Mode can change.

Step-by-step explanation:

Let us assume the data set with 10 observations

{2,6,4,3,2,6,4,9,4,7}.

Arranging data set in ascending order

{2,2,3,4,4,4,6,6,7,9}

mean=2+2+3+4+4+4+6+6+7+9/10=4.7

median

n/2=10/2=5 is an integer so,

median = average of n/2 and n/2 + 1

median = (5th value+6th value) / 2

median = (4+4) / 2=8/2=4

Mode

The most repeated value is 4. So, mode is 4 for assumed data.

Increasing highest value by 10 and decreasing lowest value by 10

{-8,2,3,4,4,4,6,6,7,19}

a.

mean=-8+2+3+4+4+4+6+6+7+19/10=4.7

Mean doesn't change

b.

median

n/2=10/2=5 is an integer so,

median = average of n/2 and n/2 + 1

median = (5th value+6th value) / 2

median = (4+4) / 2=8/2=4

Median doesn't change

c.

Most occurring value is still 4. But mode can change if the value the highest value becomes most concurring value.

a. mean = 4.7

Mean doesn't change

b.

median

n/2=10/2=5 is an integer so,

median = average of n/2 and n/2 + 1

median = (5th value+6th value) / 2

median = (4+4) / 2=8/2=4

Median doesn't change

c.

Most occurring value is 4.