Perform the exercises below with a hand calculator. When you do this, you may ge
ID: 3351097 • Letter: P
Question
Perform the exercises below with a hand calculator. When you do this, you may get variance and standard deviation answers slightly different from those given below. I obtained the answers using the sigma, which stands for standard deviation, (n-1) button. I then obtained the variance by squaring the standard deviation.
1. You have given an exam to your Jazz Dance class. Approximately one half of the class took a written version and about one half of the class took the practical exam. The scores are below:
Written scores - 92, 90, 77, 84, 77, 29, 89, 94, 83, 80, 88
Practical scores - 78, 92, 78, 64, 90, 69, 88, 79, 94, 76, 86, 78, 90
a. Calculate the measures of central tendency for each half of the class.
b. Which measure of central tendency should be used for each half of the class?
c. Which half of the class performed best?
d. Calculate the measures of variability for the groups. Which group is most homogenous?
2. You want your Bowling class to discover the effects of different types of balls on the final score. All students bowl a number of games with a 10 pound ball and then with a 16 pound ball. The scores are below:
10 pound ball scores - 190, 188, 156, 103, 102, 177, 125, 145, 166, 202, 111, 90, 85
16 pound ball scores - 201, 144, 122, 145, 163, 129, 190, 123, 189, 200, 188, 125, 177
a. Calculate the measures of central tendency for each ball.
b. Which measure of central tendency should be used for each set of scores?
c. Which ball allowed for the best scores?
d. Calculate the measures of variability for the sets of data. Which set is most scattered?
Questions 3-6 are general questions.
3. When is the median used instead of the mean?
4. What is the relationship between the standard deviation and the variance?
5. The best measure of variability to use with the mean is the __________. An inter-
quartile range is an example of an inter-___________ measure of variability.
Explanation / Answer
Answer:
1. You have given an exam to your Jazz Dance class. Approximately one half of the class took a written version and about one half of the class took the practical exam. The scores are below:
Written scores - 92, 90, 77, 84, 77, 29, 89, 94, 83, 80, 88
Practical scores - 78, 92, 78, 64, 90, 69, 88, 79, 94, 76, 86, 78, 90
a. Calculate the measures of central tendency for each half of the class.
Written
Practical
n
11
13
mean
80.2727
81.6923
median
84
79
mode
No mode
No mode
b. Which measure of central tendency should be used for each half of the class?
Median for written and Mean for practical class.
c. Which half of the class performed best?
Practical class
d. Calculate the measures of variability for the groups. Which group is most homogenous?
Written
Practical
n
11
13
sample standard deviation
17.9671
9.1686
Range
65
30
IQR
11
12
Practical class is most homogenous.
2. You want your Bowling class to discover the effects of different types of balls on the final score. All students bowl a number of games with a 10 pound ball and then with a 16 pound ball. The scores are below:
10 pound ball scores - 190, 188, 156, 103, 102, 177, 125, 145, 166, 202, 111, 90, 85
16 pound ball scores - 201, 144, 122, 145, 163, 129, 190, 123, 189, 200, 188, 125, 177
a. Calculate the measures of central tendency for each ball.
10 pound
16 pound
n
13
13
mean
141.5385
161.2308
median
145
163
mode
No mode
No mode
b. Which measure of central tendency should be used for each set of scores?
mean should be used for each set of scores.
c. Which ball allowed for the best scores?
10 pound ball allowed for the best scores.
d. Calculate the measures of variability for the sets of data. Which set is most scattered?
10pound
16pound
n
13
13
sample standard deviation
41.1777
31.0434
Range
117
79
IQR
74
60
10 pound set is most scattered.
Questions 3-6 are general questions.
3. When is the median used instead of the mean?
When there are outliers in the data median is appropriate instead of the mean.
4. What is the relationship between the standard deviation and the variance?
standard deviation is the square root of the variance.
5. The best measure of variability to use with the mean is the standard deviation. An inter-
quartile range is an example of an inter-middle 50% of measure of variability.
Written
Practical
n
11
13
mean
80.2727
81.6923
median
84
79
mode
No mode
No mode
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