Answer:
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.
