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 8.0 8.2 8.3 Mean = ______Median = ______

Night Shift 2 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 4 12 14

Deviation: ______

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 / # of values
1-20
21-40
41-60
61-80
81-100

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?