The document defines and provides examples for calculating the mean, mode, and median of a data set. The mean is the average, calculated by summing all values and dividing by the total number of data points. The mode is the value that occurs most frequently. The median is the middle value when the data is arranged in order, and is the value for which half of the data points are above and half below. Examples are provided to demonstrate calculating each measure using various data sets.

1. Topic:
Mean, Mode and Median
By:
Tania Ilham

2. Arithmetic Mean

3. Definition:
 Arithmetic Mean is the average and is computed as sum of all the
observed outcomes from the data divided by the total number of events.
 It is usually denoted by the X
 Formula:
Sum of all the observations
X = Number of the observations

4. Example 01
 The marks obtained by 6 students in a class test are 20, 22, 24, 26, 28, 30. Find
the mean ?
Solution?
Arithmetic Mean = 20+22+24+26+28+30
6
Athematic Mean = 25
Conclusion:
Hence, Arithmetic Mean of the given data is 25.

5. Example 02
 Information regarding the sale of a shop for seven days of a particular week are given
below, find Arithmetic Mean?
= 67+69+66+68+72+76+54/ 7
= 67.42 Answer
Days Sales
Monday 67
Tuesday 69
Wednesday 66
Thursday 68
Friday 72
Saturday 76
Sunday 54

6. Mode

7. Definition:
 The mode of a set of data is the number with the highest frequency.
 Formula: For Grouped Data Continuous Series
 l = lower class boundary of the modal class
 fm= frequency of the modal class.
 f1 = frequency of the class preceding the modal class.
 f2 = frequency of the class following modal class.
 h= length of class interval of the modal class.
   
hx
ffff
ff
1Xˆ
2m1m
1m




8. Example 01
 From the given below data find Mode.
 Solution:
Because, 3 repeats 14 times and it is most frequent hence 3 is
the mode OR model Value.
Value No. of items (frequency)
1 3
2 8
3 14
4 3
5 4
6 2
7 1

9. Example 02
 Frequency Distribution of Child-Care Managers Age given below, find
mode.
Class Interval Frequency
20-29 6
30-39 18
40-49 11
50-59 11
60-69 3
70-79 1

10.  Putting values:
   
hx
ffff
ff
1Xˆ
2m1m
1m



   
18 6ˆ 29.5 10
18 6 18 11
12
29.5 10
12 7
120
29.5
19
29.5 6.3 35.8
X

  
  
  

 
  

11. MEDIAN

12. Definition:
 The median is the middle score.
 If we have an even number of events we take the average of
the two middles.
 The median is defined as a value which divides a set of data
into two halves, one half comprising of observations greater
than and the other half smaller than it. More precisely, the
median is a value at or below which 50% of the data lie.
 Formula:
Median= n+1/2

13. Example 01
Calculate the median of the following data.
Solution: let us arrange the data in ascending order then form cumulative frequency.
Here Σf = n = 43
Median = n+1/2 = 43+1/2
Median = 22nd Value
No. of
students
6 16 7 4 2 8
Marks 20 25 50 9 80 40
Marks 9 20 25 40 50 80
Frequency 4 6 16 8 7 2
CF 4 10 26 34 41 43

14. Example 02
 Find the median and median class of the data given below.
Class
Boundary
15-25 25-35 35-45 45-55 55-65 65-75
Frequency
4 11 19 14 0 2

15. Solution:
Hence,
Putting Values: n/2 = 50/2 = 25
L = 35, f = 19, cf = 15, h = 10
Median = 35 + 25-15 10
19
Median = 35 + 5.263 = 40.263 Answer
Class
Boundary 15-25 25-35 35-45 45-55 55-65 65-75
Midvalue (v) 20 30 40 50 60 70
Frequency 4 11 19 14 0 2
Cumulative
Frequency 4 15 34 48 48 50