1. MEASURES OF CENTRAL TENDANCY
Submitted by,
SUPRIYA M
MATHEMATICS OPTIONAL
KUCTE, KUMARAPURAM
2. There are other types of single
values that are used to represent a given data.
Since all these values in some way or the other
represent the central values or average values
of the data, they are referred to as Measures
of Central Tendencies.
There are three types of measures of
central tendencies or Average and they are
mean, median and mode.
3. ARITHMETIC MEAN
“Arithmetic mean” or simply “mean” of a given
data is defined as the sum of all the values of the data
divided by the total number of values.
Mean is defined as
Sum of all observations
Total no:of observations
Mean is most useful when the data has no
extreme values. Extreme values distort the value of
mean due to which it is not able to represent the data
correctly.
4. Eg: The following are the marks obtained in different
subjects.
51, 62, 84, 72 and 81.
Soln: In order to get average marks scored by her in
the exam, we first add up the individual marks obtained by her in
different subjects.
51+62+84+72+81 = 350
and then divide the sum by 5,
ie, the total no:of subject.
Thus average marks scored = 350/5
= 70.
This number helps us to understand the general level of her
academic achievement and is referred to as mean.
5. MEDIAN
Median is another measure of
central tendency or another way to express
the whole data with the help of a representative
number.
6. Eg : Find the median of the following data.
3, 4, 5, 3, 6, 7, 4.
Soln: Arrange the data in ascending order
as follows.
3, 3, 4, 4, 5, 6, 7
Since the 4th term is the middle term,
hence the median of this data is 4.
Therefore, Median can be defined as the
middle value of a data when the data is arranged in
ascending order or descending order.
7. MODE
The third measure of central
tendency, ie, mode, is again a single value which
can represent the whole data.
Mode is defined to be that number
which occurs most frequently in a given data.
8. Eg:
12 eggs in a farm have the following weights.
32gm, 40gm, 27gm, 32gm, 38gm, 45gm
40gm, 32gm, 39gm, 40gm, 30gm, 31gm .
Find the mode of the above data.
Soln: First of all arrange all the weights in
ascending order as follows.
27gm, 30gm, 31gm, 32gm, 32gm, 32gm,
38gm, 39gm, 40gm, 40gm, 45gm.
Since 32gm and 40gm occur 3 times each, which
is incidentally also the largest number of times a weight
occurs in the above data, this data has two modes via
32gm and 40gm.
9. CONCLUSION
• Mean is defined as,
Sum of all observations
Total no:of observations
• When data values are arranged from the
smallest to the greatest in order, the central
value is the median.
• The most common value in a data is the mode
of the data.
