Mean, Median and Standard Deviation WS
Part One. For a summer job, you were working in the quality control department for a computer company that
manufactures computer parts. The specific part that you are to evaluate the quality of is supposed to be 8
micrometers in thickness. You obtained samples of four of these parts manufactured by the day shift and four
parts manufactured by the night shift workers. Here are the findings:
Day Shift 7.9
Night Shift 2
8.0 8.2 8.3 Mean = _________ Median = ___________
4 12
14 Mean = _________ Median = ___________
1. Determine the mean and median for each shift and compare these with the desired level of 8 micrometers.
Which shifts average was closer to the target? ___________
2. If you needed to use one of these parts in your own computer on which shift would you prefer the part to
have been manufactured? ______________ Why?
Part Two.
3. In order to describe the variability of a set of data, a simple measure is to compute the Range. In statistical
jargon, the Range is the gap between the largest and smallest value in the data set. Calculate the range for each
shift.
Day shift: Range = ___________ Night shift: Range = _____________
4. A more sophisticated way of describing the variability of a data set is based on the notion of "deviation from
the mean". For example: If the class average on a history test is 70, but you made a score of 87, your deviation
would be +17. If your friend scored a 60 on the test, his or her deviation would be -10. Give the deviation from
the mean for each part made on the night shift.
Data value:
2
Deviation:
____
4
12
14
_____ _____ ______
5. What properties do you notice about these deviations? And do you think these are true for all data sets, or just
certain types?
Part Three.
6. The commonly used measure of variability is called the "standard deviation". Supposedly, the standard
deviation tells us the size of a typical deviation from the mean for a particular set of data. Based on you answers
to #4, guess at the value of the standard deviation. ___________ . Use your notes to review how standard
deviation is calculated.
7. On the back or a separate sheet of paper, calculate the standard deviation for
a. night shift workers
b. day shift workers
Dot Plot WS
2. The heights of 20 basketball players, in inches, are given below.
68, 70, 70, 71, 75, 80, 81, 82, 84, 75, 75, 80, 75, 77, 75, 80, 83, 80, 71, 70
Make a dot plot of these results. Use a straight-edge.
Histogram WS
Create a historgram for each set of data. For the first problem, the frame is set up for you. For
#2, you will need to determine the best way to number the axes. Don’t forget to include a title
as well.
1. Chocolate candies per bag of trail mix:
50, 42, 119, 45, 68, 32, 67, 111, 61, 31, 75, 39, 62, 64, 49, 55, 51, 33, 117, 96, 64, 82
Frequency table:
Interval
1-20
21-40
41-60
61-80
81-100
# of values
2. Test scores, out of 100 points:
92, 84, 95, 77, 74, 80, 95, 70, 66, 73, 68, 90, 78, 64, 72, 78, 75, 65, 59, 71, 77, 92, 91, 89, 74,
76, 90
Frequency Table
Interval
# of values
Box Plot WS
1. The numbers below represent eighteen-hole scores of golfers at Crystal Springs Golf Club.
88 80 80 77 84 74 80 79 83 77 75 75 78 79 77 81 72 85 75 76 78 76 77 72 75 70
List the numbers in order from least to greatest:
Mean___________________
Lower Quartile______________
Lower Extreme____________
Upper Quartile______________
Upper Extreme____________
Interquartile Range___________
Make a box plot in the line provided. Be sure to label all 5 parts.
2. The wait times for several local doctor offices (in minutes) are listed below.
11, 20, 21, 20, 10, 65, 14, 12, 16, 18
What is the outlier?_______________
Find the mean and median WITH the outlier.
Mean______________
Median___________
Find the mean and median WITHOUT the outlier.
Mean______________
Median___________
Two-Way Frequencies WS
The table represents a survey of what 50 people did with their leisure time. Answer all questions with
complete sentences.
Dance
Sports
Movies
TOTAL
Women
16
6
8
30
Men
2
10
8
20
TOTAL
18
16
16
50
1.) In each box in the table above write the appropriate percentages.
2.) What percentage of those surveyed are involved in leisure activities that require physical
exercise?
3.) What percent of those surveyed dance?
What percentage of men dance?
4.) What percent movie watchers are men?
5.) What percent of men and women play sports of those surveyed?
6.) What percent of women play sports or dance?
7.) Of those that dance or play sports, what percent are men?
8.) What percent of men watch movies?
9.) If you want to open an exercise gym would you advertise more to men or women or both
equally?