The document discusses measures of central tendency including the mean, median, and mode for ungrouped data sets. The mean is the average and is calculated by adding all values in the data set and dividing by the number of values. The median is the middle number when data is arranged in order. For even data sets, the median is the average of the two middle numbers. The mode is the number that occurs most frequently in the data set. Sometimes there are multiple modes or no mode. The range is the difference between the highest and lowest values in the data set.

1. Mean , Median and Mode
for Ungrouped Data
By
Sharmin Abeer

2. Measures of Central Tendency
Measures of central tendency are numerical
descriptive measures which indicate the center of a
distribution or data set. There are three common
measures of central tendency:
the mean
the median
the mode

3. Mean
is the sum of all the measurements divided
by the number of measurements in the set
This is also known as average
it is denoted by (“x bar”)

4.  For example
Data Set=2,5,9,3,5,4,7
Number of Elements in Data Set=7
5
7
35
7
)7453952(



x

5. Median
 Median is the number present in the middle when
the number in a set of data are arranged in
ascending or descending order
 The median of a data set is dependent on whether the
number of element in the data set is odd or even

6.  For example,
5,3,9,2,7,5,8
Organizing in ascending order
2,3,5,5,7,8,9
Here n=7(an odd number)
Median=5

7. For example,
Data set:2,5,9,3,5,4
Organizing in ascending order
2,3,4,5,5,9
Here , n=6
Median=4+5/2=4.5

8. Mode
The mode is the number that occurs the most
For example,
2,5,9,3,5,4,7
Mode=5

9. Sometimes a set of data will have more than one
mode
For example,
2,9,5,7,8,6,4,7,5
Here,5 and 7 are both mode

10. Sometimes there is no mode in a set of data
 for example,
3,8,7,6,12,11,2,1
All the number in this set occur only once therefore
there is no mode in this set

11. Range
The range of a set of data is the difference between
the largest and the smallest number in the set
For example,
40,50,60,55,66,20,80
80-20=60
The range is 60

12. Thank you all