KNR 445
Statistics in Science & Technology

Assignment
Measures of Variability

The purpose of this lab is to introduce the procedures for calculating measures of variability, a measure of how scores are distributed. You will use the data file of CDC data including the variable "Region".

Measures of Variability

Three measures of central tendency are the mode, the median and the mean. Three measures to summarize how scores are distributed are also used: the range, the interquartile range, and the standard deviation.

Homework
1.      Each of five raw scores is converted to a deviation score.  The values for four of the deviation scores are as follows: -4, +2, +3, -6.  What is the value of the remaining deviation score?

 2.      For each of the following statistics, what would be the effect of adding one point to every score in a distribution?  What generalization do you make from this?  (Do this without calculations.)
(a)          mode
(b)         median
(c)          mean
(d)         range
(e)          variance
(f)           standard deviation 

3.      Imagine that each of the following pairs of means and standard deviations was determined from scores on a 50-item test.  With only this information, describe the probable shape of each distribution.  (Assume a normal distribution unless you believe the information presented suggests otherwise.)
(a)           = 29, S = 3
(b)          = 29, S = 4
(c)           = 48, S = 4
(d)          = 50, S = 0

 4.      Given: X = 500 and S = 100 for the SAT.
(a)          What percentage of scores would you expect for fall between 400 and 600?
(b)         between 300 and 700?
(c)          Between 200 and 800?

5.      The mean is 67.2 for a large group of students in a college physics class; Duane obtains a score of 73.
(a)          From this information only, how would you describe his performance?
(b)         Suppose S = 20.2. Now how would you describe his performance?
(c)          Suppose S = 2.2. Now how would you describe his performance?

 6.      Imagine you obtained the following results in an investigation of sex differences among high school students: 

 (a)          What is the pooled standard deviation for mathematics achievement?
(b)         What is the pooled standard deviation for verbal ability?
(c)          Compute the effect size for each of these mean differences.

What is your impression of the magnitude of the two effect sizes?

SPSS Questions

1. Find and list the procedures in SPSS which allow you to calculate the measures of central tendency and variability.

2. Calculate the range, interquartile range, and the standard deviation for the variable Region.
    a. What type of data is the variable "Region"?
    b. Interpret the measures of variability from the SPSS output.
    c. Which, if any, of the measures is most appropriate for this type of data?
SPSS Output for question 2

3. This question will use the data in the variable Smoker Deaths.
    a. Calculate the population mean and standard deviation for the variable Smoker Deaths. Present the measures in a paragraph, following the format presented in class (see Powerpoint notes).
    b. For each of your six regions, calculate the mean and standard deviation of the variable Smoker Deaths. Create a figure presenting the parameters (If your SPSS does not have Graphs==>Interactive, use Excel).
        i. Is the region with the largest mean the same as the region with the largest standard deviation? Is there any reason why the largest mean should be associated with the largest standard deviation?
        ii. Which region has the most variability in Smoker deaths? Which has the least variability in Smoker deaths? Justify your answers.
   c. Compare the population SD to the individual region SDs:
        i. How many region SDs are equal to the population SD?
        ii. How many region SDs are less than the population SD?
        iii. How many region SDs are greater than the population SD?
SPSS Output for Question 3

4. This question will use the data in the variable Tax per Pack:
    a. Calculate the population measures of central tendency and variability for the variable Tax per Pack.
    b. Create a new variable, TaxUp, by multiplying each state tax by 10, and calculate the measures of central tendency and variability for this new variable.
    c. Create a new variable, TaxDown, by dividing each state tax by 10, and calculate the measures of central tendency and variability for this new variable.
    d. Create a new variable, TaxAddUp, by adding 10 to each state tax, and calculate the measures of central tendency and variability for this new variable.
    e. Create a new variable, TaxSubDn, by subtracting 10 from each state tax, and calculate the measures of central tendency and variability for this new variable.
    f. Compare the mean and SD values calculated in a, b, c, d and e.
    g. Repeat the step above for the median and interquartile range.
    h. Draw a conclusion regarding the effect on the measures of central tendency and variability of
        i. adding/subtracting a constant to all values, and
        ii. Multiplying/dividing all values by a constant
SPSS Output for Question 4