1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 6.1 Statistics: Mean, Median, Mode, and Range

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Objectives o Understand statistical terms. o Calculate mean, median, mode, and range.

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Statistical Terms Terms Used in the Study of Statistics Data: Value(s) measuring some characteristic of interest such as income, height, weight, grade point averages, scores on tests, and so on. (We will consider only numerical data.) Mean: The sum of all the data divided by the number of data items. (Also called the arithmetic average.)

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Statistical Terms Terms Used in the Study of Statistics (cont.) Median: The middle data item. (Arrange the data in order and pick out the middle item.) Mode: The single data item that appears the most number of times. (Some data may have more than one mode. We will leave the discussion of such a situation to a course in statistics. In this text, if the data have a mode, there will be only one mode.) Range: The difference between the largest and smallest data items.

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Finding the Mean Find the mean income for the families in Group A. Group A: Annual Income for 8 Families $28,000 $22,000 $25,000 $27,000 $45,000 $80,000 $25,000 $30,000 Solution Find the sum of the 8 incomes and divide by 8.

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Finding the Mean (cont.)

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Finding the Mean (cont.) For Group A: The mean annual income is $35,250. (You may want to use a calculator to do this arithmetic).

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Calculating Mean, Median, Mode, and Range To Find the Median 1.Arrange the data in order. 2.If there is an odd number of items, the median is the middle item. 3.If there is an even number of items, the median is the average of the two middle items.

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Finding the Median Find the median income for Group A and the median GPA for Group B. Group A: Annual Income for 8 Families $28,000$22,000$25,000$27,000 $45,000$80,000$25,000$30,000 Group B: Grade Point Average (GPA’s) for 11 Students 2.0 1.93.13.52.9 2.53.62.02.43.4

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Finding the Median (cont.) Solution The data in Group A are not in order, so we arrange the set to be in order: Group A (in order): $22,000; $25,000; $25,000; $27,000; $28,000; $30,000; $45,000; $80,000

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Finding the Median (cont.) There are 8 items (an even number) so we find the middle two items and average them: These items are the 4th and 5th items. (Count 4 from the left and 4 from the right.) The data are $27,000 and $28,000:

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Finding the Median (cont.) Group B (in order): 1.9; 2.0; 2.0; 2.0; 2.4; 2.5; 2.9; 3.1; 3.4; 3.5; 3.6 For Group B, there are 11 items (an odd number) and the median is the 6th item. So the median is 2.5.

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Finding the Mode and Range Find the mode and the range for both Group A and Group B (See Examples 1 and 2). Solution The mode is the most frequent item. From the arranged data in Example 2, we can see that: for Group A, the mode is $25,000. for Group B, the mode is 2.0.

14. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Finding the Mode and Range (cont.) The range is the difference between the largest and smallest items: Group A range = $80,000  $22,000 = $58,000. Group B range = 3.6  1.9 = 1.7.

15. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems Two sets of data, Group A and Group B, are given. Find the following statistics for each group. a.mean b. median c. mode d. range Group A: Body Temperature (in Fahrenheit degrees) of 8 People Group B: The Time (in minutes) of 11 Movies

16. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problem Answers