Standard Deviation of Grouped Data

1. Standard Deviation of Grouped Data Standard deviation can be found by summing the square of the deviation of each value, or, If the value is present more than once, the square of the deviation can be calculated once and multiplied by the frequency of occurrences

2. Standard Deviation of Grouped Data • Find the sample standard deviation of the following data: • 7, 6, 7, 6, 7, 8, 5, 6, 7, 5, 7, 8, 9, 7

3. Standard Deviation of Grouped Data • Find the sample standard deviation of the following data: • 7, 6, 7, 6, 7, 8, 5, 6, 7, 5, 7, 8, 9, 7

4. Standard Deviation of Grouped Data • Find the sample standard deviation of the following data: • 7, 6, 7, 6, 7, 8, 5, 6, 7, 5, 7, 8, 9, 7

5. Standard Deviation of Grouped Data • Find the sample standard deviation of the following data: • 7, 6, 7, 6, 7, 8, 5, 6, 7, 5, 7, 8, 9, 7

6. Standard Deviation of Grouped Data • Find the sample standard deviation of the following data: • 7, 6, 7, 6, 7, 8, 5, 6, 7, 5, 7, 8, 9, 7

7. Standard Deviation of Grouped Data • Find the sample standard deviation of the following data: • 7, 6, 7, 6, 7, 8, 5, 6, 7, 5, 7, 8, 9, 7

8. Standard Deviation of Grouped Data • The calculator also gives 1.122

9. Standard Deviation of Grouped Data • We grouped the data in the above example. • The same process can be used when given data in the form of a histogram or pie chart. • Since the values of the specific data points has been lost,assume all the data points within a cell have the same value as the cell midpoint. • The student is left to review Example 10 on page 77.

10. Standard Deviation of Grouped Data • Assume the histogram on the following slide represents our data. • Make a table of values (x values – the midpoint of each column), including the frequency of each column. • Calculate the sample standard deviation of the data represented in the histogram

11. Standard Deviation of Grouped Data • The cell midpoints are 1, 2, 3, 4, and 5 • The frequencies are 2, 3, 5, 4, and 1

12. Standard Deviation of Grouped Data • The cell midpoints are 1, 2, 3, 4, and 5 • The frequencies are 2, 3, 5, 4, and 1

13. Standard Deviation of Grouped Data • The cell midpoints are 1, 2, 3, 4, and 5 • The frequencies are 2, 3, 5, 4, and 1

14. Standard Deviation of Grouped Data • The cell midpoints are 1, 2, 3, 4, and 5 • The frequencies are 2, 3, 5, 4, and 1 What does this add to?

15. Standard Deviation of Grouped Data • The cell midpoints are 1, 2, 3, 4, and 5 • The frequencies are 2, 3, 5, 4, and 1 What does this add to?

16. Standard Deviation of Grouped Data • The cell midpoints are 1, 2, 3, 4, and 5 • The frequencies are 2, 3, 5, 4, and 1 What does this add to?

17. Standard Deviation of Grouped Data • The cell midpoints are 1, 2, 3, 4, and 5 • The frequencies are 2, 3, 5, 4, and 1

18. Standard Deviation of Grouped Data • The cell midpoints are 1, 2, 3, 4, and 5 • The frequencies are 2, 3, 5, 4, and 1

19. Standard Deviation of Grouped Data • The cell midpoints are 1, 2, 3, 4, and 5 • The frequencies are 2, 3, 5, 4, and 1

20. Standard Deviation of Grouped Data • How can we do this in our calculator? • Put the “x” values in L1 • Put the frequency in L2 • Stat • Calc • 1-Var Stats • 2nd L1, 2nd L2, Enter

21. Homework • Pg 81 & 82, # 29 – 32 all (4)