STATISTICS MATH 221
FINAL EXAM
REVIEW QUESTIONS
SOLUTIONS GUIDE (WITH PROF. HEARD’S
COMMENTS IN BLUE)
1. Explain the difference between a population and a sample. In
which of these is it important to distinguish between the two in order
to use the correct formula? mean; median; mode; range; quartiles;
variance; standard deviation.
Solution: A sample is a subset of a population. A population consists
of every member of a particular group of interest. The variance and
the standard deviation require that we know whether we have a
sample or a population.
Be able to identify Populations and Samples in a problem. For
example, 389 American 3rd Graders were asked what their favorite ice
cream was. 69% answered chocolate. The sample would be the 389
American 3rd Graders, the population would be “All American 3rd
Graders.”
2. The following numbers represent the weights in pounds of six 7-
year old children in Mrs. Jones' 2nd grade class.
{25, 60, 51, 47, 49, 45}
Find the mean; median; mode; range; quartiles; variance; standard
deviation.
Solution: mean = 46.166....
median = 48
mode does not exist
range = 35
Q1 = 45
Q2 = median = 48
Q3 = 51
variance = 112.1396
standard deviation =10.59
Looking at this problem, understand what changing a minimum or
maximum value does to the mean, median, mode and range. For
example, if you replaced the minimum value of 25 with “40” your
mean changes, but your median does not! Also your range is greatly
affected by changing the minimum (or maximum) values because that
is the way the range is calculated (Max Value – Min Value). The mode
,would depend on if other data points were duplicated with the
replacement.
3. If the variance is 846, what is the standard deviation?
Solution: standard deviation = square root of variance = sqrt(846) =
29.086
Also, if the Standard Deviation is 29.086, what is the variance? It’s
(29.086)^2 or 845.9954 or 846 rounded.
4. If we have the following data
34, 38, 22, 21, 29, 37, 40, 41, 22, 20, 49, 47, 20, 31, 34, 66
Draw a stem and leaf. Discuss the shape of the distribution.
Solution:
2|219200
3|48714
4|0197
5|
6|6
This distribution is right skewed (positively skewed) because the “tail”
extends to the right.
Remember turn it counter clockwise 90 degrees to see the distribution.
, 5. What type of relationship is shown by this scatter plot?
Solution: Weak positive linear correlation
You can see the upward trend but the dots are clinging together very
well.
6. What values can r take in linear regression? Select 4 values in this
interval and describe how they would be interpreted.
Solution:
the values are between –1 and +1 inclusive.
-1 means strong negative correlation
+1 means strong positive correlation
0 means no correlation
.5 means moderate positive correlation
etc.
I like to say the following (next page):
FINAL EXAM
REVIEW QUESTIONS
SOLUTIONS GUIDE (WITH PROF. HEARD’S
COMMENTS IN BLUE)
1. Explain the difference between a population and a sample. In
which of these is it important to distinguish between the two in order
to use the correct formula? mean; median; mode; range; quartiles;
variance; standard deviation.
Solution: A sample is a subset of a population. A population consists
of every member of a particular group of interest. The variance and
the standard deviation require that we know whether we have a
sample or a population.
Be able to identify Populations and Samples in a problem. For
example, 389 American 3rd Graders were asked what their favorite ice
cream was. 69% answered chocolate. The sample would be the 389
American 3rd Graders, the population would be “All American 3rd
Graders.”
2. The following numbers represent the weights in pounds of six 7-
year old children in Mrs. Jones' 2nd grade class.
{25, 60, 51, 47, 49, 45}
Find the mean; median; mode; range; quartiles; variance; standard
deviation.
Solution: mean = 46.166....
median = 48
mode does not exist
range = 35
Q1 = 45
Q2 = median = 48
Q3 = 51
variance = 112.1396
standard deviation =10.59
Looking at this problem, understand what changing a minimum or
maximum value does to the mean, median, mode and range. For
example, if you replaced the minimum value of 25 with “40” your
mean changes, but your median does not! Also your range is greatly
affected by changing the minimum (or maximum) values because that
is the way the range is calculated (Max Value – Min Value). The mode
,would depend on if other data points were duplicated with the
replacement.
3. If the variance is 846, what is the standard deviation?
Solution: standard deviation = square root of variance = sqrt(846) =
29.086
Also, if the Standard Deviation is 29.086, what is the variance? It’s
(29.086)^2 or 845.9954 or 846 rounded.
4. If we have the following data
34, 38, 22, 21, 29, 37, 40, 41, 22, 20, 49, 47, 20, 31, 34, 66
Draw a stem and leaf. Discuss the shape of the distribution.
Solution:
2|219200
3|48714
4|0197
5|
6|6
This distribution is right skewed (positively skewed) because the “tail”
extends to the right.
Remember turn it counter clockwise 90 degrees to see the distribution.
, 5. What type of relationship is shown by this scatter plot?
Solution: Weak positive linear correlation
You can see the upward trend but the dots are clinging together very
well.
6. What values can r take in linear regression? Select 4 values in this
interval and describe how they would be interpreted.
Solution:
the values are between –1 and +1 inclusive.
-1 means strong negative correlation
+1 means strong positive correlation
0 means no correlation
.5 means moderate positive correlation
etc.
I like to say the following (next page):
