Significance of Central Tendency in Statistical Analysis
Understanding the importance of central tendency in statistics such as mean, median, and mode. Learn how these measures provide a representative score of a group, indirect insight into populations, and aid in comparing the performance of different groups. Dive into the calculations and methods for determining central tendency in both ungrouped and grouped data sets.
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Presentation Transcript
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 6100 115-119 4 117 468 M ean==-------- 101.67 110-114 6 112 672 60 105-109 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--CF 110-114 6 53 Md = l + ----------- x CI 105-109 8 47 f 100-104 15 39 95-99 10 24 90-94 7 14 60/2---24 85-89 4 7 =99.5+ -------------- x 5 80-84 3 3 15 ------ 30 24 60 99.5 + ---------- x 5 30 =99.5+ ------ 15 = 99.5+2 Median-- =101.5 15
MODE Gilford 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 5 7 8 9 10 11 13 14 15 20 6 Mo. 4 3 2 4 1 1 1 1 1 Mode= 3XMedian 2 Mean
