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Measure of Central Tendency

Measure of Central Tendency. Vernon E. Reyes. A single number that repreresents the average. Useful way to describe a group Central tendency – it is generally located towards the middle or center of the distribution where most of the data tend to be concentrated

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Measure of Central Tendency

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  1. Measure of Central Tendency Vernon E. Reyes

  2. A single number that repreresents the average • Useful way to describe a group • Central tendency – it is generally located towards the middle or center of the distribution where most of the data tend to be concentrated • Well-known measures of central tendency are: mode, the median, and the mean

  3. Plot

  4. Plot

  5. Mode • The mode (Mo) is the only measure of central tendency used for NOMINAL DATA like religion, college major • It can also describe any level of measurement • The Mo is found through INSPECTION rather than COMPUTATION

  6. Example • 2 3 1 1 6 5 4 1 4 4 3 What id the Mo? = ____ Note: the Mo is NOT the frequency (f = 4) (Mo = 1)

  7. The mode can be unimodal or bimodal

  8. Median • When ordinal or interval data are arranged in order or size, its possible to locate the median (Md or Mdn) – the middlemost point in a distribution • The position of the median value can be located by inspection or by formula • Position of the median = N+1 / 2

  9. Odd or Even • For odd number of cases (N) the median is easy to find 11 12 13 16 17 20 25 Using the formula (7+1) / 2 = 4 Therefore the fourth place is the median which is equal to 16

  10. Odd or Even • For even number of cases (N) the median is always the point above or below where 50% of the cases will fall. 11 12 13 16 ! 17 20 25 26 Using the formula (8+1) / 2 = 4.5 Therefore the fourth place is the median which is equal to 16.5

  11. Other note! • If the data are not in order from low to high (or high to low), you should put them in order first before trying to locate the median!

  12. The MEAN • The arithmetic mean X = mean (read as x bar X = raw score N = Total number of score Σ = sum (greek capital letter sigma)

  13. Mo vs Md vs Mean • “center of gravity” • A number that is computed which balances the scores above and below it To understand the meaning of the MEAN we must look at the deviation DEVIATION = X – X Where X = any raw score X = mean of the distribution

  14. ------------------------------ X X – X ----------------------------- 9 +3 8 +2 6 0 5 -1 2 -4 X = 6 Notice that if we add all the deviations it will always equal to zero! (+)5 + (-)5 = 0 Later we shall discuss standard deviation example +5 - 5

  15. ------------------------------ X X – X ----------------------------- 1 2 3 5 6 7 X = ? Find the mean! Find the deviations! Another example

  16. The Weighted Mean • The mean of means! Example: Section 1: X 1 = 85 N 1 = 28 Section 2: X 2 = 72 N 2 = 28 Section 3: X 3 = 79 N 2 = 28 85 + 72 + 79 = 236 3 3 = 78.97

  17. Formula for weighted mean with unequal sizes Xw = Σ Ngroup Xgroup Ntotal Xw = N1X1 + N2X2 +N3X3 Ntotal

  18. The Weighted Mean • The mean of means! Example: unequal N Section 1: X 1 = 85 N 1 = 95 Section 2: X 2 = 72 N 2 = 25 Section 3: X 3 = 79 N 2 = 18 95(85) + 25(72) + 18(79) = 8075+1800+1422 138 138 11,297 138 = 81.86

  19. Lets compare Mean, Median and Mode!

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