Descriptive Statistics, Graphing, Statistical Analysis

1. Name three measures of central tendency and state a disadvantage of using each method.

2. Which measure(s) of central tendency are not useful for the data below? Why?
   3, 6, 4, 7, 9, 3, 5, 102, 8

3. Which measure(s) of central tendency is (are) not useful for the data below? Why? 
   0, 0, 0, 7.2, 7.3

4. Calculate the mean, median, and mode for the data below.
   3, 6, 4, 7, 9, 3, 5, 102, 8

5. Calculate the mean, median, and mode of the following data:
   3, 6, 4, 2, 2, 1

6. Calculate the following for the data below.
   64, 75, 72, 68, 66, 66

7. Suppose that you plot the weight of students in a class and obtain a bell shaped curve. You calculate a mean weight and a standard deviation. How can this information be used to provide you with a range of weights that includes 95% of the students?

8. Suppose that a researcher takes a sample of insects from a field and discovered that the mean length of the insects is 10.4 mm. The standard deviation is 1.5. What range of sizes will include 95% of the insects in the field?

9. Suppose that a researcher takes samples of mice from around New York State and discovers that the mean weight of the mice in the sample is 27 g and the standard deviation is 3 grams. Based on these data, what is the weight range of 95% of the mice in New York State?

10. Suppose that a researcher wished to display a graph of the number of each kind of insect found in a field. Explain why a line graph is not appropriate for this type of data.

11. Suppose that a researcher measured air temperature in a forest every hour for 24 hours. What kind of graph would be most appropriate for this data? 
    a) bar graph     b) line graph     c) scatter plot

12. Suppose that a researcher wished to learn if a certain drug slows the growth of tumors. She obtained mice with tumors and randomly divided them into two groups. She then injected one group of mice with the drug and used the second group as a control. After 2 weeks, she sacrificed the mice and weighed the tumors. The mean weight of tumors for each group of mice is below.
    
    Drug group      = 0.39 g
    Control group = 0.42 g
    She used a 1-tailed t-test. The probability (p) = 0.012.
    
    What should she conclude? Why?

13. Suppose that a researcher wishes to learn whether the pH of soil affects seed germination of a particular herb found in forests near her home. She believes that acid soils (low pH) will have less germination. She filled 10 flower pots with acid soil (pH 5.5) and ten flower pots with neutral soil (pH 7.0) and planted 100 seeds in each pot. The mean number of seeds that germinated in each type of soil is below.

    acid soil: 42.5 seeds germinated per pot
    neutral soil: 51.1 seeds germinated per pot

    She used a 1-tailed t-test. The probability (p) = 0.082.

    What should she conclude? Why?

14. Suppose that a researcher wished to learn if a particular chemical is toxic to a certain species of beetle. She believes that the chemical might interfere with the beetle’s reproduction. She obtained beetles and divided them into two groups. She then fed one group of beetles with the chemical and used the second group as a control. After 2 weeks, she counted the number of eggs produced by each beetle in each group. The mean egg count for each group of beetles is below.

Chemical group           = 32.5 eggs

Control group             = 43.1 eggs

She used a 1-tailed t-test. The probability (p) = 0.072.

What should she conclude? Why?