Question

For the data 1, 5, 7 x + 1, 9 ,x-2, 3. If the mean is 4 then find the value of x. hence, find the mode

Answer 1

4=(1+5+7x+1+9+x-2+3)/6
solve and get x.

Where,

6=Number of terms.

Answer 2

Given data is 1,5,7,x + 1, 9, x - 2 and 3.

Here, Total number of observations = 7.

Given mean = 4.

We know that mean = (sum of observations)/(Total number of observations).

⇒ 4 = (1 + 5 + 7 + x + 1 + 9 + x - 2 + 3)/7

⇒ 4 = (2x + 24)/7

⇒ 28 = 2x + 24

⇒ 2x = 4

⇒ x = 2.

So,

⇒ x + 1 = 3

⇒ x - 2 = 0.

Now,

The new data is 1,5,7,3,9,0,3.

We know that mode is the number which appears often in a set of numbers.

In the above list, the number 3 occurs most often.

Therefore, the mode is 3.

Hope this helps!