MEASURES OF CENTRAL TENDENCY ARITHMETIC MEAN.pptx

A short description on the arithmetic mean of the measures of central tendency and how to find the arithmetic mean of the ungrouped data , Grouped data and in the step deviation method

1. MEASURES OF CENTRAL TENDENCY ARITHMETIC MEAN

2. AGENDA Introduction Arithmetic Mean Ungrouped data Grouped data Step deviation method

3. Introduction In statistics, a measure of central tendency is a single value or number that attempts to describe or represent a set of data by identifying the central position within that set of data.

4. Arithmetic Mean The arithmetic mean is the simplest and most widely used measure of a mean, or average. It simply involves taking the sum of a group of numbers, then dividing that sum by the count of the numbers used in the series.

5. Arithmetic Mean – Ungrouped data Mean x̄ =∑x/n Where ‘n’ is the total number of observations. Problem :The marks obtained by 6 students in a class test are 20, 22, 24, 26, 28, 30. Find the mean x̄ = (20+22+24+26+28+30)/6 Mean = 150/6 Mean = 25 .

6. Arithmetic Mean – Grouped data Mean x̄ = ∑ fx /N Where f = frequency, x = the value of the variable and N=the sum of frequency or N = ∑f Problem : Calculate A.M. from the following data Marks obtained 4 8 12 16 20 No.of.students 6 12 18 15 9

7. Arithmetic Mean – Grouped data Marks obtained (x) No.of.students (f) fx 4 6 24 8 12 96 12 18 216 16 15 240 20 9 180 Total ∑f = N = 60 ∑ fx =756

8. Arithmetic Mean – Grouped data From the formula , Mean x̄ = ∑ fx /N By applying the values in the formula , we get x̄ = 756 / 60 Mean x̄ = 12.6.

9. Step deviation method Mean = Where A = assumed mean, c = common size of class intervals, f = frequency of the class interval, d = deviation, x = midpoint of the class intervals

10. Step deviation method Class interval Frequency(f) Midpoint (x) d = (x - A)/c fd 20-30 3 25 -4 -12 30-40 1 35 -3 -3 40-50 18 45 -2 -36 50-60 10 55 -1 -10 60-70 4 65 70-80 1 75 1 1 80-90 3 85 2 6 90-100 2 95 3 6 Total N = 42 ∑ fd = -48 c = 10 A = 65 d = (x - A)/c d=(25 - 65)/10 d = (-40)/10 d = (-4)

11. Step deviation method A = 65 C = 10 ∑f = 42 ∑f d = -48 By applying the values in the formula , we get x̄ = 65 + ( (-48) / 42) x 10 x̄ = 65 + (-1.143) x 10 x̄ = 65 + (-11.43) x̄ = 65 - 11.43 Mean x̄ = 53.57

12. Thank you YOGESHWARAN