1. In your own words, define and discuss the importance of measures of dispersion or variability in statistical analyses. How do they differ from measures of central tendency?2. A researcher wants to

1. In your own words, define and discuss the importance of measures of dispersion or variability in statistical analyses. How do they differ from measures of central tendency?

2. A researcher wants to know about the primary type of drug used by students on a college campus. Her data is in the table below.

Primary Drug Used by Students

Drugf

Marijuana1250

Cocaine/crack175

Heroin250

Hallucinogens70

Other385

·         a) Calculate the variation ratio for the data above.

·         b) Describe and interpret your findings.

3. Ten rookie police officers started working at the Pine Valley Police Dept in 2005. At that time, they all began with the same salary ($36,000/year). Today, 10 years later, the salaries of those same 10 officers are the following:

Police Officer Salaries 10 Years Posthire

OfficerSalary ($)

148,000

248,000

350,000

451,000

552,000

654,000

757,000

858,000

962,000

1069,000

·         a. Calculate the range, variance, and standard deviation of the data above. Describe the results.

·         b. How would you explain the variation (or difference) in salaries?

1.       Dispersion is defined as the measure of variation of items. Some of the measures of dispersion or variability which are used in statistical analysis are standard deviation, range, variance, inter quartile range etc. The measure of dispersion is used to find out the spread of the data or its variation around the central value, to control undesired variability, to test the reliability of average etc. One of the difference between them are central tendency indicates the central value of distribution where measure of dispersion indicates the variation of observation around that central value.

2.       A) Variation ratio for the data is 0.413.

B) Marijuana is the most commonly used primary drug among the students on a college campus. The variation ratio of the data suggests that mode is the best method used. Here the mode value corresponds to the drug Marijuana.

                3.            A) Range = 9,21,000

                                Variance = 95567433333

                                Standard deviation = 309139.8281

The range of salaries after 10 years is $921000 and its variance is 95567433333 which shows variability from its mean value.

                                B) The salaries of the ten police officers increased much during the ten years. Even though ten police officers start with the salary $36000/annum, now each of them has different scale of salary with a range of $921000. The bar diagram shows the variation of salary during the ten years.