Question

For the data in the following sample: 10, 6, 8, 6, 5


a. Find the mean and the standard deviation.
b. Now change the score of X=10 to X=0 , and find the new mean and standard deviation.
c. Describe how one extreme score influences the mean and standard devation.

Answer 1

Answer:

a.

mean=7

standard deviation=2

b.

mean=5

standard deviation=3

c.

Due to one extreme score, our center of location changes and there comes more variability in the data measured through standard deviation.

Step-by-step explanation:

a.

Mean= sum of values/number of values

Mean=(10+6+8+6+5)/5

Mean=7

$Standard deviation=\sqrt{\frac{{sum(x-xbar)^2} }{n-1}}$

x     x-xbar  (x-xbar)²

10    3              9  

6    -1               1

8     1               1

6    -1               1

5    -2            4

sum(x-xbar)²=9+1+1+1+4=16

sum(x-xbar)²/n-1=16/4=4

Standard deviation=√4

Standard deviation=2

b.

Mean= sum of values/number of values

Mean=(0+6+8+6+5)/5

Mean=25/5

Mean=5

$Standard deviation=\sqrt{\frac{{sum(x-xbar)^2} }{n-1}}$

x     x-xbar  (x-xbar)²

0    -5              25  

6     1                1

8     3               9

6    1                 1

5    0               0

sum(x-xbar)²=25+1+9+1+0=36

sum(x-xbar)²/n-1=36/4=9

Standard deviation=√9

Standard deviation=3

c)

We can see that by adding one extreme value 0 our mean decreases from 7 to 5 and standard deviation increases from 2 to 3. This means that our center of location changes and there comes more variability in the data measured through standard deviation.