Download Unit 4 Statistics: Data Analysis Mean

Unit 4 Statistics: Data Analysis
Mean-average of a set of data. Add up the terms and divide by the number of terms. The mean is a
measure of central tendency. It’s main limitation is that it is affected by outliers.
Median-the number that occurs in the middle of data that is in order. It is also a measure of central
tendency.
Mode-the number that occurs the most in a set of data. It is a measure of central tendency. You can
have more than one mode or no mode.
Variance-measure of variability. The spread of the data.
Standard Deviation-square root of the variance. A measure of variability.
Normal Distribution-is a set of data that follows a symmetrical, bell shaped curve. Most of the data is
close to the mean.
Empirical Rule
68% of the data lies within 1 std deviation of the mean.
95% of the data lies within 2 std deviations of the mean.
99.7% of the data lies within 3 std deviations of the mean.
Sample-Part of the population. Used when it is impossible or impractical to collect data for an entire
population. As sample size increases, the amount of variance among the sample means decreases.
Review Examples
1.) Jesse is the manager of a guitar shop. He recorded the number of guitars sold each week for a
period of 10 weeks. His data is shown in the table.
Week
# of Guitars
Sold
1
2
3
4
5
6
7
8
9
10
12
15
20
8
15
18
17
21
10
24
a. What is the mean of Jesse’s data?
b. What are the variance and the standard deviation of Jesse’s data?
c. If an outlier is defined as any value that is more than two standard deviations from the mean,
which, if any, values in Jesse’s data would be considered an outlier?
2.) Anne is the regional sales manager for a chain of guitar shops. She recorded the number of
guitars sold at two stores in her region each week for one year (52 weeks). These histograms
show the data Anne collected.
a. Estimate the mean and standard deviation for each store.
b. What is the range of possible means for each store?
c. Explain why the empirical rule is or is not a good fit for each store.
3.) Anne, the regional manager for the chain of guitar shops in the previous review example, took 10
random samples from her data about the number of guitars sold at each of the two shops per
week during the last year. The sample means for each shop are as follows:
Shop 1: {21.25, 15.25, 25.0, 15.0, 14.0, 18.0, 12.25, 19.25, 22.0, 21.25}
Shop 2: {17.5, 18.25, 8.0, 22.25, 7.75, 18.25, 24.0, 28.5, 16.0, 16.25}
a. What was the sample size that Anne used?
b. What is the mean and standard deviation for each set of samples?
EOCT Practice Items
1.) This table shows the scores of the first six games played in a professional basketball league.
Winning
Score
Losing
Score
110
98
91
108
109
116
101
88
84
96
77
114
The winning margin for each game is the difference between the winning score and the losing score.
What is the standard deviation of the winning margins for these data?
a.
b.
c.
d.
3.8 points
8.3 points
9.5 points
12.0 points
2.) This frequency table shows the heights for Mrs. Quinn’s students.
Height (in inches)
42
43
44
45
46
47
48
Frequency
1
2
4
5
4
2
1
What is the approximate standard deviation of these data?
a. 1.0 in
b. 1.5 in
c. 2.5 in
d. 3.5 in
3.) Kara took 10 random samples of the winning margins for each of two professional basketball
teams. The sample size was 4. The distributions of the sample means are shown in these
histograms.
Which is the best estimate of the standard deviation for both samples?
a.
b.
c.
d.
Team 1:
Team 1:
Team 1:
Team 1:
3.75 points; Team 2: 2.2 points
7.4 points; Team 2: 4.4 points
15 points; Team 2: 8.8 points
10 points; Team 2: 10 points
4.) John took 10 random samples of the winning margins for each of two professional basketball
teams. The distributions of the sample means are shown in these histograms.
Based on John’s data, which statement is MOST likely true?
a.
b.
c.
d.
Both the sample mean and sample standard deviation are greater for team 1 than for team 2.
The sample means for both are equal, but the sample standard deviation for Team 1 is greater.
The sample means for both are equal, but the sample standard deviation for team 2 is greater.
Both the sample mean and the sample standard deviation for team 2 is greater.
5.) Mary took 10 random samples of the winning margins for each of two professional basketball
teams. The sample were taken from all 82 games in one season. The distributions of the sample
means are shown in these histograms.
Which question can be answered based on Mary’s data?
a.
b.
c.
d.
Which team had the greater number of all-star players?
Which team won more games?
Which team won by a more consistent margin?
Which team lost more games by a narrow margin?
6.) In a set of 10 random samples of winning scores for games played in a professional basketball
league, the sample size is 6, the sample mean is 97.5 points, and the sample standard deviation is
5.2 points. Which expression represents the estimated standard deviation of all the winning
scores?
5.2
10
b. 5.2 10
5.2
c.
6
d. 5.2 6
a.