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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.

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standard deviation of grouped data

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

standard deviation of grouped data2
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
standard deviation of grouped data3
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
standard deviation of grouped data4
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
standard deviation of grouped data5
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
standard deviation of grouped data6
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
standard deviation of grouped data7
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
standard deviation of grouped data8
Standard Deviation of Grouped Data
  • The calculator also gives 1.122
standard deviation of grouped data9
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.
standard deviation of grouped data10
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
standard deviation of grouped data11
Standard Deviation of Grouped Data
  • The cell midpoints are 1, 2, 3, 4, and 5
  • The frequencies are 2, 3, 5, 4, and 1
standard deviation of grouped data12
Standard Deviation of Grouped Data
  • The cell midpoints are 1, 2, 3, 4, and 5
  • The frequencies are 2, 3, 5, 4, and 1
standard deviation of grouped data13
Standard Deviation of Grouped Data
  • The cell midpoints are 1, 2, 3, 4, and 5
  • The frequencies are 2, 3, 5, 4, and 1
standard deviation of grouped data14
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?

standard deviation of grouped data15
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?

standard deviation of grouped data16
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?

standard deviation of grouped data17
Standard Deviation of Grouped Data
  • The cell midpoints are 1, 2, 3, 4, and 5
  • The frequencies are 2, 3, 5, 4, and 1
standard deviation of grouped data18
Standard Deviation of Grouped Data
  • The cell midpoints are 1, 2, 3, 4, and 5
  • The frequencies are 2, 3, 5, 4, and 1
standard deviation of grouped data19
Standard Deviation of Grouped Data
  • The cell midpoints are 1, 2, 3, 4, and 5
  • The frequencies are 2, 3, 5, 4, and 1
standard deviation of grouped data20
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
homework
Homework
  • Pg 81 & 82, # 29 – 32 all (4)