1. Basic Tools For economic Analysis. Frequency Distribution: This refers to the arrangement of data or information in the tabular form to reflect their frequencies. The scores of 30 students in maths test in s s 1 can be presented a frequency distribution. 89 5 9 5 8 9 4 5 6 6 7 9 5 3 8 9 5 97 6 8 9 7 8 3 2 4 1 1.

2. Ungrouped Frequency Distribution Score (x)FrequencyCumulative Frequency 122 213 325 427 5512 6315 7318 8523 9730 ∑F=30

3. Ungrouped Frequency Distribution The Marks scored by twenty students in Biology test are written below; 1, 5, 6, 5, 6, 8, 3, 0, 8, 4 1, 5, 4, 6, 8, 2, 7, 1, 6, 2 Required: Summarize the scores into a frequency distribution. Solution

4. Solution to the above question Score (X)TallyFrequencyCumulative Frequency 0111 111134 21126 3117 4 29 5111312 61111417 7878 1 111 1 3 ∑F20 18 20

5. Measures of Central Tendency The three measures of central tendency are: Mean, Mode and Median. It should be noted that these three types of averages are also called measures of location 1. MEAN (Arithmetic Mean) This is the sum of series of figures divided by the number of times the figures appeared. Symbolically, the arithmetic mean is represented by ẍ and pronounced “X” bar. The formular for mean is ẍ = ∑X/n Where ẍ = Arithmetic mean ∑ = sum of. Pronounced Sigma ∑X = sum of the values of series of figures n= number of figures or element Eg. Find the mean of the following nombers 3, 5, 6, 7, 4, 6, 6 and 5. solution. First we add up the numbers thus 3+5+6+7+4+6+6+5=42. ∑X=42 N=8 ẍ =42/8= 5.25

6. MEAN cont’d Mean is also obtained from a frequency distribution table using the formular ẍ = ∑FX/ ∑F Where ẍ =mean ∑FX=sum of the product of the scores and frequency ∑F=sum of the frequencies. Eg. In a physics test 8 students scored 30%, 11 scored 40%, 6 scored 50 %, 3 scored 55% and 2 scored 60%. What is the mean score of the students? Solution

7. solution Score (x)Frequency (F)Fx (F×X) 308240 4011440 506300 553165 602120 ∑F=30∑FX=1265 ẍ =∑FX/ ∑F = 1265/30 =42.2 ans

8. The Median The median of a set of numbers arranged in either ascending or descending order is the value of the middle number. For an odd set of numbers median is calculated as Me=(nt1/2) th number, where me =median N=number of items or scores.

9. Median cont’d For an even set of numbers median is calculated as Me=(n/2) th +(n/2+1) th term Eg 1. Calculate the median of the following set of scores 60, 40, 45, 30, 80, 85, 65, 50, 55 Solution: Rearrange 30, 40, 45, 50, 55, 60, 65, 80, 85 median =55.

10. Example 2 Median Cont’d Find the median of the following set of marks 60, 45, 40, 55, 50, 85, 90, 30, 65, 80 Solution Rearrange: 30, 40, 45, 50, 55, 60, 65, 80, 85, 90. Me= (10/2)th +(10/2+1) th scores = 5 th +(5+1)th scores 5+6 th /2 50+60/2= 115/2 =57.5 ans

11. Assignment 1)-Find the mean of the following data a) 3 4 8 5 4 5 6 7 3 6 7 8 b) 4 7 6 4 2 5 8 9 4 7 5 6 2) Find the median of the following data a) 2 5 6 7 8 9 3 2 9 5 b) 3 7 5 8 4 9 3 5 6