Measures Of Central Tendency

MEASURES OF CENTRAL TENDENCY Is the easiest way in summarizing the data.

THE MEAN • The mean is the simplest and most efficient measures of central tendency. • It is the value obtained by adding the values in the distribution and dividing the sum by the total number of values. 3 classifications of the mean 5. Mean for ungrouped data. 6. Mean for grouped data. 7. Weighted mean.

Mean for Ungrouped data: 1. Consider the following values. Compute for the value of the mean. 21, 10, 36, 42, 39, 52, 30, 25, and 26. _ x/n x=

∑

= 21 + 10 + 36 + 42 + 39 + 52 + 30 + 25 + 26 / 9 = 281 / 9 = 31.22

Mean for grouped data: the midpoint method •

Classes 11 - 22 23 – 34 35 – 46 47 – 58 59 – 70 71 – 82 83 – 94

f 3 5 11 19 14 6 2 Σ = 60

x 16.5 28.5 40.5 52.5 64.5 76.5 88.5

fx 49.5 142.5 445.5 997.5 903.0 459.0 177.0 Σ = 3 ,174

Χ = Σ fx / n = 3,174/60 = 52.90

Unit deviation method •

Classes f d 11-22 3 -3 23-34 5 -2

fd -9 -10

35-46 47-58 59-70 71-82 83-94

-11 0 14 12 6

11 19 14 6 2

-1 0 1 2 3

Σ = 60

Σ fd = 2

_ x = Χ a + (Σ fd / n ) c = 52.5+(2/60)12 = 52.90

Weighted mean 1. Suppose a student in a certain college is enrolled in 6 subjects where not all of the subjects carry a 3 unit load. Assuming further, that the student was able to obtain the following grades as shown.

subject 1 2 3 4 5 6

no. of units (x) 3 3 5 1 2 3

grades (y) 2.0 3.0 1.25 3.0 2.5 2.5

_ x= Σxy / Σx = 3(2.0) + 3(3.0) + 5(1.25) + 1(3.0) + 2(2.5) + 3(2.5)________________ 3+3+5+1+2+3 = 36.75 17 _ x = 2.16

GENERALIZATION In your own words define measures of central tendency, then state the formula in finding the mean for grouped and ungrouped data, as well as the formula in finding the weighted mean.

EVALUATION • Find the mean for the following given set of data. 1. The daily sales of ABC Enterprises for the first 7 days of a certain month are shown below. Php5,286, Php10,826, Php2,580, Php6,386, Php4,650, Php3,635, and Php8,625. determine the daily mean sales of the store for the first seven days?

2. Consider the FDT of the ages of 75 mayor’s then compute the mean age of the mayor’s? Classes F 25-30 3 31-36 6 37-42 11 43-48 27 49-54 16 55-60 7 61-66 4 67-72 1

N= 75

3. A Die was rolled 100 times and the results are shown below. outcome (x) frequency (y) 1 17 2 14 3 20 4 15 5 15 6 19 compute the value of the weighted mean?