One hundred teachers attended a seminar on mathematical problem solving. The attitudes of a representative sample of 12 of the teachers were measured before and after the seminar. A positive number for change in attitude indicates that a teacher's attitude toward math became more positive. The 12 change scores are as follows:
3
8
–1
2
0
5
–3
1
–1
6
5
–2
What is the mean change score?
What is the standard deviation for this population?
What is the median change score?
Find the change score that is 2.2 standard deviations below the mean.
Refer to
[link] determine which of the following are true and which are false. Explain your solution to each part in complete sentences.
The medians for all three graphs are the same.
We cannot determine if any of the means for the three graphs is different.
The standard deviation for graph b is larger than the standard deviation for graph a.
We cannot determine if any of the third quartiles for the three graphs is different.
True
True
True
False
In a recent issue of the
IEEE Spectrum , 84 engineering conferences were announced. Four conferences lasted two days. Thirty-six lasted three days. Eighteen lasted four days. Nineteen lasted five days. Four lasted six days. One lasted seven days. One lasted eight days. One lasted nine days. Let
X = the length (in days) of an engineering conference.
Organize the data in a chart.
Find the median, the first quartile, and the third quartile.
Find the 65
th percentile.
Find the 10
th percentile.
Construct a box plot of the data.
The middle 50% of the conferences last from _______ days to _______ days.
Calculate the sample mean of days of engineering conferences.
Calculate the sample standard deviation of days of engineering conferences.
Find the mode.
If you were planning an engineering conference, which would you choose as the length of the conference: mean; median; or mode? Explain why you made that choice.
Give two reasons why you think that three to five days seem to be popular lengths of engineering conferences.
A survey of enrollment at 35 community colleges across the United States yielded the following figures:
Organize the data into a chart with five intervals of equal width. Label the two columns "Enrollment" and "Frequency."
Construct a histogram of the data.
If you were to build a new community college, which piece of information would be more valuable: the mode or the mean?
Calculate the sample mean.
Calculate the sample standard deviation.
A school with an enrollment of 8000 would be how many standard deviations away from the mean?
Enrollment
Frequency
1000-5000
10
5000-10000
16
10000-15000
3
15000-20000
3
20000-25000
1
25000-30000
2
Check student’s solution.
mode
8628.74
6943.88
–0.09
Use the following information to answer the next two exercises.X = the number of days per week that 100 clients use a particular exercise facility.
x
Frequency
0
3
1
12
2
33
3
28
4
11
5
9
6
4
The 80
th percentile is _____
5
80
3
4
The number that is 1.5 standard deviations BELOW the mean is approximately _____
0.7
4.8
–2.8
Cannot be determined
a
Suppose that a publisher conducted a survey asking adult consumers the number of fiction paperback books they had purchased in the previous month. The results are summarized in the
[link] .
# of books
Freq.
Rel. Freq.
0
18
1
24
2
24
3
22
4
15
5
10
7
5
9
1
Are there any outliers in the data? Use an appropriate numerical test involving the
IQR to identify outliers, if any, and clearly state your conclusion.
If a data value is identified as an outlier, what should be done about it?
Are any data values further than two standard deviations away from the mean? In some situations, statisticians may use this criteria to identify data values that are unusual, compared to the other data values. (Note that this criteria is most appropriate to use for data that is mound-shaped and symmetric, rather than for skewed data.)
Do parts a and c of this problem give the same answer?
Examine the shape of the data. Which part, a or c, of this question gives a more appropriate result for this data?
Based on the shape of the data which is the most appropriate measure of center for this data: mean, median or mode?
