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### Problems: Measuring Dispersion

1. John and Jane have five children whose ages are 1, 3, 7, 9 and 10.

a) What are the mean, median, and modal ages of these children?
b) What is the range and standard deviation of these ages? (Show how you get the answer.)

2. Mike has started running, hoping to run a marathon in six months. For the last six days, his running times (in minutes) have been: 39, 43, 68, 40, 49, 61.

a) Compute the mean, median, and mode of these data.
b) Compute the range and standard deviation.

3. Gretchen has caught six lake trout. These are their weights:
20 oz, 24 oz, 30oz, 28 oz, 18 oz, 18 oz.

a) Compute the mean, median, and mode of these data.
b) Compute the range and standard deviation.

4. Joan has collected data on gasoline prices from six area stations: \$1.09 \$1.11 \$1.27 \$1.13 \$1.15 \$1.15

a) Compute the mean, median, and mode of these data.
b) Compute the range and standard deviation.

5. You have a sample of eight items. You have computed the mean, and the following are seven of the deviations from the mean: -1, -2, 4, 7, -3, -1, -2. What is the variance of this sample?

6. If the standard deviation of a group of numbers is zero, what can you conclude?

7. The table below gives the percentile ranks of the cumulative grade point averages for the junior class as the end of the 1975-76 school year.

 Percentile: GPA 90 3.72 80 3.53 75 3.40 50 3.01 25 2.54 20 2.44 10 2.14
a) What is the interdecile range?
b) What is the median?

8. Suppose the students at Apex College have a mean SAT verbal plus math score of 950 with a standard deviation of 250. At nearby Apogee University the students have an average SAT total of 1000 with a standard deviation of 100. How would you explain the differences in the student bodies of these two schools to someone who did not know what the mean and standard deviation were?

(Most of these questions can be easily answered using a statistical program or by using statistical calculators. A site on the Internet that has a calculator to answer these is http://25yearsofprogramming.com/javascript/descriptivestatistics.htm.)