MEASURES OF CENTRAL TENDENCY AND DISPERSION AROUND THE MEAN

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MEASURES OF CENTRAL TENDENCY AND DISPERSION
AROUND THE MEAN
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Activity 1

• e) 50,42857143
• f) 7
• Mean height 182,2cm
• Mean mass 80kg
• a) 1996 13,27
• 1997 15,55
• 1998 19,07
• b) The percentage of women in SA infected
• with HIV increased from 1996 to
• 1998.
• a) 135 454,4444 km2

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Measures of Dispersion around the Mean

• IQR is generally considered as a measure of
  spread around the median.
• Variance and Standard Deviation are measures of
  dispersion around the mean.
• A deviation from the mean considers how far each
  element in the data set differs from the mean.

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• Variance is the average of the squares of the
  deviations of each data item from the mean.
• Large variance data items are widely spread.
• Small variance data items are closely clustered
  around the mean.

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Activity 2

• a) 20 years
• b) 20 years
• Fred variance 4,67
• Sipho variance 162,67

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Standard Deviation

• The Standard Deviation is the Square Root of
  Variance.
• Standard Deviation

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Activity 3

1. 11 years
2. 196 n 10
3. 4,43 years (to two decimal places)

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Using the Calculator to find the Standard
Deviation

• To work out the Standard deviation for Freds
  sister, press the following keys
• MODE 2STAT
• 1 1-VAR
• 22 17 21
• AC
• SHIFT 1 (STAT)
• 5 VAR
• 3
• You should get 2,16

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• Now try for Siphos sisters.
• This tells us that Siphos sisters ages are more
  spread out than Freds.

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Activity 4

• a) (i) -6,6c
• (ii) 12,8c
• b) The temperatures are spread out.
• c)
• a) 48,8 y
• b) 10,3 y
• c)

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The Standard Deviation and the Mean
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Activity 5

• Jabu 12
• Mmatsie 12
• Jabu 5,2 (to one decimal place)
• Mmatsie 0,8 (to one decimal place)
• Although these two students have the same
  average, Mmatsie is more consistent. Jabu does
  well in some tests and badly in others.

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Using Standard Deviations to reach Conclusions

• Provided that the sample size is reasonably large
  and the data is not too skewed (that is, it does
  not have some very large or very small values),
  it is possible to make the following approximate
  statements
• About 66 lie within one standard deviation of
  the mean.
• About 95 lie within two standard deviations of
  the mean.
• Almost all of the data will lie within three
  standard deviations of the mean.

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Activity 6

• a) 22 calls
• b) 5,3 calls
• 225,3
• Interval is (16,7 27,3)
• The phone calls on Tues, Wed and Fri fall within
  the interval.
• 60