Standard Deviation

1
Standard Deviation

• A measure of variability
• Commonly used to calculate other statistical
  measures
• Shows the distance (difference) between the mean
  and the steepest part of a normal curve
• Indicates dispersion, or spread, of scores in a
  distribution

2
Standard Deviation

• The smaller the standard deviation, the more
  tightly clustered the scores
• The larger the standard deviation, the more
  spread out the scores

3
Standard Deviation

• On an average day in Los Angeles, the number of
  sudden deaths from cardiac causes is about 4.6.
  On the day of the Northridge earthquake, there
  were 25 such deaths, 24 of which occurred after
  431 a.m., when the earthquake struck.

4
Standard Deviation

• Make your prediction
• Will the average male or the average female who
  died from sudden cardiac causes on the day of the
  earthquake be older?
• A. the average female was older
• B. the average male was older

5

• Predict whether the ages of the males or the ages
  of the females who died on the day of the
  earthquake were more variable.
• A. ages of males were more variable
• B. ages of females were more variable

6
The Data

• Ages of females who died
• 66
• 92
• 75
• 84
• 83
• 80

• Ages of males who died
• 90 38 59
• 45 47 67
• 79 75 66
• 71 68 62
• 51 55 62
• 56 56 64

7
Calculate the Mean

• 66
• 92
• 75 480/6 80
• 84
• 83
• 80
• 480

• 90 38 59
• 45 47 67
• 79 75 66
• 71 68 62
• 51 55 62
• 56 56 64
• 1111
• 1111/18 61.7

8
Subtract the mean from each score

• X - X s
• 66 80 -14
• 92 80 12
• 75 80 -5
• 84 80 4
• 83 80 3
• 80 80 0

• s s2
• -142 196
• 122 144
• - 52 25
• 42 16
• 32 9
• 02 0
• 399 (sum of squares)

9
Find the variance find the square root of the
variance

• There it is! The standard deviation for the ages
  of the females who died that day is 8.93.
• Now you try the same formula for the ages of the
  males.

• ?s2/N (N-1)
• 399/5 79.8
• sd ?s2
• ?79.8 8.93