Step-by-step explanation:

Given:-

In mathematics test given to 10 students the following marks (out of 100) are

recorded: -

11, 09, 40, 37, 90, 40, 95, 55, 40, 65 .

To find:-

Find the mean, median and mode of this

data

Solution:-

Mean:-

Given observations are:

11, 09, 40, 37, 90, 40, 95, 55, 40, 65

SUM of all observations

= 11+9+40+37+90+40+95+55+40+65

=482

NUMBER of all observations = 10

We know that

Mean = Sum of all observations/Number of all observations

=> Mean = 482/10

Mean = 48.2

Median :-

Given observations are:

11, 09, 40, 37, 90, 40, 95, 55, 40, 65

On writing them into ascending order

09, 11 , 37 , 40, 40, 40, 55 ,65 , 90 , 95

Number of all observations = 10

It is an even number

We know that

The number of observations is n an even number then median is the average of the (n/2)th and

(n/2)+1 th observations

n/2 th observation

=> 10/2

= 5th observation = 40

6th observation = 40

Median = (40+40)/2

Median = 80/2

Median = 40

Mode :-

Given observations are:

11, 09, 40, 37, 90, 40, 95, 55, 40, 65

On writing them into ascending order

09, 11 , 37 , 40, 40, 40, 55 ,65 , 90 , 95

Most occuring observation = 40

40 occurs 3 times

Mode = 40

Answer:-

1)Mean = 48.2

2)Median = 40

3)Mode = 40

Used formulae:-

• Mean = Sum of all observations/Number of all observations

• The number of observations is n an even number then median is the average of the (n/2)th and
• (n/2)+1 th observations

• Mode is the most frequent occuring observation of the given data.