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Practice 1: Center of the Data

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

Summary: This module provides students with opportunities to apply concepts related to descriptive statistics. Students are asked to take a set of sample data and calculate a series of statistical values for that data.

Student Learning Outcomes

  • The student will calculate and interpret the center, spread, and location of the data.
  • The student will construct and interpret histograms an box plots.

Given

Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars.

Complete the Table

Table 1
Data Value (# cars) Frequency Relative Frequency Cumulative Relative Frequency
       
       
       
       
       
       

Discussion Questions

Exercise 1

What does the frequency column sum to? Why?

Solution

65

Exercise 2

What does the relative frequency column sum to? Why?

Solution

1

Exercise 3

What is the difference between relative frequency and frequency for each data value?

Exercise 4

What is the difference between cumulative relative frequency and relative frequency for each data value?

Enter the Data

Enter your data into your calculator or computer.

Construct a Histogram

Determine appropriate minimum and maximum x and y values and the scaling. Sketch the histogram below. Label the horizontal and vertical axes with words. Include numerical scaling.

An empty graph template for use with this question.

Data Statistics

Calculate the following values:

Exercise 5

Sample mean = x¯ x =

Solution

4.75

Exercise 6

Sample standard deviation = sx s x =

Solution

1.39

Exercise 7

Sample size = nn =

Solution

65

Calculations

Use the table in section 2.11.3 to calculate the following values:

Exercise 8

Median =

Solution

4

Exercise 9

Mode =

Solution

4

Exercise 10

First quartile =

Solution

4

Exercise 11

Second quartile = median = 50th percentile =

Solution

4

Exercise 12

Third quartile =

Solution

6

Exercise 13

Interquartile range (IQRIQR) = _____ - _____ = _____

Solution

6 - 4 = 2 6 - 4 = 2

Exercise 14

10th percentile =

Solution

3

Exercise 15

70th percentile =

Solution

6

Exercise 16

Find the value that is 3 standard deviations:

  • a. Above the mean
  • b. Below the mean

Solution

  • a. 8.93
  • b. 0.58

Box Plot

Construct a box plot below. Use a ruler to measure and scale accurately.

Interpretation

Looking at your box plot, does it appear that the data are concentrated together, spread out evenly, or concentrated in some areas, but not in others? How can you tell?

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