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# Measure of Central Tendency - PowerPoint PPT Presentation

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

Vernon E. Reyes

• 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

• 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

• 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)

• 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

• 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

• 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

• 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!

• The arithmetic mean

X = mean (read as x bar

X = raw score

N = Total number of score

Σ = sum (greek capital letter sigma)

• “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

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

X X – X

-----------------------------

1

2

3

5

6

7 X = ?

Find the mean!

Find the deviations!

Another example

• 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

Xw = Σ Ngroup Xgroup

Ntotal

Xw = N1X1 + N2X2 +N3X3

Ntotal

• 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