Importance of central tendency------

1-- It is Representative score of group

2-- Indirect description of the population

3-- Comparison of performance of two group

Type of central tendency 1--MEAN

2—MEDIAN

3—MODE

Measures of central Tendency

• Measures of central tendency

• Measure of central tendency is a statistical calculation from a set of independent observation and measurement of a certain item or entry and intended totypify the observation.

• English &English•

MEAN---The arithmetic mean , or more simply the mean ,is the sum of the separate scores or measures divided by their number. Garrett

Calculation of mean when data are ungrouped

Formula 0f mean

Where IS----- M=EX/N M=Mean X=Score E=Sum of score N=No. of score

Scores M 80+20+16+12==128/4== 32

Calculation of Mean from grouped data (long method)

Formula of mean (Long Method) Where is------ M= Efx/N M=mean f==frequency X=Midpoint of class interval N==no offrequency

CI f x fx

120-124 3 122 366 6100115-119 4 117 468 M ean==-------- 101.67110-114 6 112 672 60105-109 8 107 856 100-104 15 102 1530 95-99 10 97 970 Mean=101.67 90-94 7 92 644 85-89 4 87 348 80-84 3 82 246 ____ _________ N=60 Efx=6100

Median

When ungrouped scores or other measures are arranged in order of size ,the median is the midpoint in the series. Garrett.

Median is the value that separates all the cases in a ranked distribution into halves. Warren.

Median is that score in the ranked distribution which has exactly half of the cases below it and half of above it. English &English

Calculation of median when data are ungrouped

N+1 7+1 Mdn = ------------ -----------= 4= 18 2 2

16, 10,18,22,19,21,17 =

10,16,17,18,19,21,22= 7+1/2=8/4=4th item Median =18

Calculation of median when data are grouped

CI f Cf 120-124 3 60 115-119 4 57 N/2--CF110-114 6 53 Md = l + ----------- x CI105-109 8 47 f100-104 15 3995-99 10 2490-94 7 14 60/2---2485-89 4 7 =99.5+ -------------- x 580-84 3 3 15

------ 30—24 60 99.5 + ---------- x 5 15 30 =99.5+ ------ 15 = 99.5+2 Median-- =101.5

MODEGilford—In a distribution of group data, the crude mode is the mid –point of the class interval having the greatest frequency.

10,13,10,7,9,5,7,10,5,7,5,8,8,9,5,10,9,10,9,12,13,14,13,10,11,20,15

Mode= 3XMedian –2 Mean

5 7 8 9 10 11 13 14 15 20

4 3 2 4 6Mo.

1 1 1 1 1