Mean Median Mode in Grade X

Whenever you talk about Mean, Median , mode, range, standard deviation, variance these are all are the part of Statistics. It provides the basic knowledge about all these things. So let’s discuss these statistical topics for grade X of cbse board.

Firstly we will study about mean , mode and median and range. we also see the relation between them, so let’s start with Definition of Mean.

Mean is the average value of the any given series for example

Find the mean of the series given below

2,5,7,9,11

Mean of the series will be sum of all the values divide by number of values

2+5+7+9+11/5

34/5

6.8 is the mean for given series and for more examples click here.

Now, we will talk about mode

Mode is the value which always occurs most frequently in the observation.  The mode of frequency division is the value of variable which has maximum frequency.

Now we will talk about median

Median is the value which divides the sample into two equal parts

Median can be calculated for a given series as

2,3,7,9,11,34,45

For calculating median we need to see the number of terms. There are two formulas which are given below

If terms in the series are odd

Median =n+1/2

Where n is the number of term in the series

If terms in the series are even then

Median = (n/2 +n/2+1)th term/2

Now for the above problem number of terms are 7 that is odd so

Median =7+1/2

Median =4

So median will be 4^th term that is 9

Note : we need to put the series in ascending order. We have not converted above series in ascending order because its already in ascending order.

if the number of terms is even

2,7,4,5,8,11

Now firstly we need to put that series in ascending order.

2,,4,5,7,8,11

Now n=6 so n is even so we will apply the formula for even terms

(6/2 +6/2+1)th /2

(3^rd +4^th )/2

5+7/2

6 so six will be the median

Now there is relation between mean, mode and median.

Mode =3median – 2mean

The same formula can be written as

Mean =3/2median-1/2mode

Or median = 1/3mode + 2/3mean

Now we will see some problems

Example : if mode=6 and mean =5 then find median

So we have the formula

Median = 1/3*6 +1/2*5

Median=2 + 2.5

Median =4.5

Example2 If mean =6 and median =7 then find mode

We have the formula

Mode =3median -2mean

Mode=3*7 -2*6

Mode =21-12

Mode =9

Example 3

If median =4 and mode =2 find mean

Mean =3/2 median -1/2 mode

Mean=3/2*4 -1/2*2

Mean =6-1

Mean =5

Now I think you have well understood about mean mode and median now we will move to standard deviation and variance

Firstly we will talk about variance

Statistical variance is a way of measuring how the data distributes itself on the mean or expected value. And if we talk about standard deviation then it is the square root of variance.

Now we will see how to calculate standard deviation and variance.

Find the value of standard deviation and variance. of given series

25,24,25,30

Firstly we will find the mean

25+24+25+30/4

104/4

26

Now subtract every number from mean and then do the square of every number and then add

(25-26)² +(24-26)²+(25-26)² +(30-26)²

 1 +4+1 +16/4

22/4

5.5

Standard  deviation will be the square root of variance.

so it will be √5.5

This is all about Mean, Median , mode, range, standard deviation, variance from Math Blog on Grade X. For more information on this topic and Math Blog on Grade XI you can visit different websites.