2.7 Measures of the spread of the data -- rrc math 1020  (Page 9/25)

Refer to [link] determine which of the following are true and which are false. Explain your solution to each part in complete sentences.

1. The medians for all three graphs are the same.
2. We cannot determine if any of the means for the three graphs is different.
3. The standard deviation for graph b is larger than the standard deviation for graph a.
4. We cannot determine if any of the third quartiles for the three graphs is different.

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.

1. Organize the data in a chart.
2. Find the median, the first quartile, and the third quartile.
3. Find the 65 ^th percentile.
4. Find the 10 ^th percentile.
5. Construct a box plot of the data.
6. The middle 50% of the conferences last from _______ days to _______ days.
7. Calculate the sample mean of days of engineering conferences.
8. Calculate the sample standard deviation of days of engineering conferences.
9. Find the mode.
10. 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.
11. 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:

6414; 1550; 2109; 9350; 21828; 4300; 5944; 5722; 2825; 2044; 5481; 5200; 5853; 2750; 10012; 6357; 27000; 9414; 7681; 3200; 17500; 9200; 7380; 18314; 6557; 13713; 17768; 7493; 2771; 2861; 1263; 7285; 28165; 5080; 11622

1. Organize the data into a chart with five intervals of equal width. Label the two columns "Enrollment" and "Frequency."
2. Construct a histogram of the data.
3. If you were to build a new community college, which piece of information would be more valuable: the mode or the mean?
4. Calculate the sample mean.
5. Calculate the sample standard deviation.
6. A school with an enrollment of 8000 would be how many standard deviations away from the mean?

The 80 ^th percentile is _____

1. 5
2. 80
3. 3
4. 4

The number that is 1.5 standard deviations BELOW the mean is approximately _____

1. 0.7
2. 4.8
3. –2.8
4. Cannot be determined

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] .

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.
2. If a data value is identified as an outlier, what should be done about it?
3. 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.)
4. Do parts a and c of this problem give the same answer?
5. Examine the shape of the data. Which part, a or c, of this question gives a more appropriate result for this data?
6. Based on the shape of the data which is the most appropriate measure of center for this data: mean, median or mode?