MATHS

PRESENTATION

1

MEAN DEFINITION

To find the mean: Add up all the numbers and then divide by the total number of items in the set. For example, the mean of 1, 2, 6, 8, 10

Formula of MeanMean = ( X1 + X2 + X3 + . . . + Xn ) / n

= [ Σ Xi ] / n

Mean =(1+2+6+8+10) /5 =27/5 = 5.4

➢3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29The sum of these numbers is 330These are fifteen numbers.The mean is equal to 330 / 15 = 22The mean of the above numbers is 22

➢ Find the mean of the following :

S.No Income (in Rs) No of employees (fixi)

1 500 4 2000

2 520 10 5200

3 550 6 3300

4 600 5 3000

5 800 3 2400

6 1000 2 2000

𝛴𝑓ⅈ = N = 30 ∑𝑓ⅈ𝑥ⅈ = 17900

Mean = ∑𝑓ⅈ𝑥ⅈ

𝛴𝑓ⅈ= 17900 / 30 = Rs. 596.67

Weight (in Kg) (x) 56 70 60 57

No of students (f) 12 13 4 11

➢Find the mean 12, 34, 45 ,56, 67, 78, 89

➢Find the mean of the following table

➢Find Mean of 3 , 7 , 5 , 13 , 25

The median is a simple measure of central tendency. To find the median, we

arrange the observations in order from smallest to largest value. If there is an

odd number of observations, the median is the middle value. If there is an

even number of observations, the median is the average of the two middle

values.

MEDIAN DEFINATION

+1

(

)

➢Find the median

7, 4, 6, 11, 18, 19, 20

▪ Here n = 7

Rearrange the data in ascending order , we get

4, 6, 7, 11, 18, 19, 20

Median = 𝑛+1 𝑡ℎ

2=

7+1 𝑡ℎ

2=

8

2= 4𝑡ℎ 𝑡𝑒𝑟𝑚

➢ Find the median

31, 38, 27, 28, 36, 25, 35, 40

▪ Here n = 8

Rearrange the data in ascending order , we get

25, 27, 28, 31, 35, 36, 38, 40

There are eight values , so the median is halfway between the fourth and fifth

values

Median = 31+35

2=

66

2= 33

➢ Obtain the median of the following frequency :

x f c.f

1 8 8

2 10 18

3 11 29

4 16 45

5 20 65

6 25 90

7 15 105

8 9 114

9 6 120

N = 120

▪ Here N = 120

N/2 = 120 / 2 = 60

We find the cumulative frequency just greater than N / 2 , is 65

and the value of x corresponding to 65 is ‘5’. Therefor median is ‘5’

➢ Obtain the median of the following frequency distribution

x : 1 2 3 4 5 6 7 8 9

f : 8 10 11 16 20 25 15 9 6

➢ Find the median of the values

15, 14, 45, 56, 67, 11, 12

The number which appears most often in a set

of numbers is called mode.

MODE DEFINATION

Example of Mode

➢Find mode of series

30 32 34 36 38 40 42 40 32 40

Mode =40

➢ Find mode

3, 3, 4, 5, 8, 6, 5, 11, 32, 3

▪ Arrange the data in the form of a frequency table, we have

Value : 3 4 5 6 8 11 32

frequency : 3 1 2 1 1 1 1

since the value 3 occurs the maximum no of times . Hence the modal value

is 3

➢ Find the mode of the following distribution

size (in inch) : 30 32 34 36 38 40 42

No of shirts sold : 8 17 30 35 18 7 3

▪ 35 shirts are sold of size 36” and this is the maximum no

i.e Mode of this distribution = 36

➢The age of 9 persons are

48, 42, 47, 48, 56, 65, 56, 65, 60

(a) Find the model age

(b) While copying a student wrote 65 in place of one 56 . Find the model age

➢Find the mode

33, 43, 45, 54, 43, 33, 23, 32, 33