Question

A set of eight score are given as: 3,2,6,3,x,3,10,5. The mean of these number is 2 more than the mode. find the value of x

Answer 1

Given :

• A set of eight score are given as: 3,2,6,3,x,3,10,5.
• Mean is 2 more than the mode.

To Find :

The value of x.

Solution :

Analysis :

Here first we have to find the mean from the mode. Then by using the formula of mean we can find the value of x.

Required Formula :

Mean = Sum of observations/Total no of observations

Explanation :

We know that mode is the variate which has maximum frequency.

Here in the given data 3,2,6,3,x,3,10,5; 3 is repeated 3 times. Hence, 3 is having the maximum frequency.

So,

Mode = 3.

Now,

It is said that mean is 2 more than mode.

∴ Mean = Mode + 2

= 3 + 2

= 5

Mean = 5.

We know that if we are given the observations, the mean and is asked to find a missing value then our required formula is,

Mean = Sum of observations/Total no of observations

where,

• Total no of observations = 8
• Mean = 5

Using the required formula and substituting the required values,

⇒ Mean = Sum of observations/Total no of observations

⇒ 5 = (3 + 2 + 6 + 3 + x + 3 + 10 + 5)/8

⇒ 5 = (32 + x)/8

⇒ 5 × 8 = 32 + x

⇒ 40 = 32 + x

⇒ 40 - 32 = x

⇒ 8 = x

∴ x = 8.

The value of x is 8.

Verification :

LHS :

⇒ Sum of observations/Total no of observations

⇒ (3 + 2 + 6 + 3 + x + 3 + 10 + 5)/8

• Putting x = 8,

⇒ (3 + 2 + 6 + 3 + 8 + 3 + 10 + 5)/8

⇒ 40/8

⇒ 5

∴ 5.

RHS :

∴ 5.

∴ LHS = RHS.

• Hence verified.