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MEASURES OF CENTRAL TENDENCY AND DISPERSION AROUND THE MEAN

MEASURES OF CENTRAL TENDENCY AND DISPERSION AROUND THE MEAN. 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 km 2.

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MEASURES OF CENTRAL TENDENCY AND DISPERSION AROUND THE MEAN

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  1. MEASURES OF CENTRAL TENDENCY AND DISPERSION AROUND THE MEAN

  2. 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

  3. 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.

  4. 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.

  5. Activity 2 • a) 20 years b) 20 years • Fred: variance = 4,67 Sipho: variance = 162,67

  6. Standard Deviation The Standard Deviation is the Square Root of Variance. Standard Deviation =

  7. Activity 3 • 11 years • = 196 n = 10 • 4,43 years (to two decimal places)

  8. Using the Calculator to find the Standard Deviation • To work out the Standard deviation for Fred’s sister, press the following keys: [MODE] [2:STAT] [1: 1-VAR] 22 [=] 17 [=] 21 [=] [AC] [SHIFT] [1] (STAT) [5: VAR] [3: ] [=] You should get 2,16

  9. Now try for Sipho’s sisters. This tells us that Sipho’s sisters ages are more spread out than Fred’s.

  10. Activity 4 • a) (i) -6,6°c (ii) 12,8°c b) The temperatures are spread out. c) • a) 48,8 y b) 10,3 y c)

  11. [Hodge,S & SeeSons, Glasgow, page 78] The Standard Deviation and the Mean

  12. 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.

  13. 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.

  14. Activity 6 • a) 22 calls b) 5,3 calls • = 22±5,3 Interval is (16,7 ; 27,3) The phone calls on Tues, Wed and Fri fall within the interval. 60%

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