Arithmetic

Central Tendency

Easy

If the mean of five observations x + 1, x + 2, x + 3, x + 4 and x + 5 is 15, then what is the mean of the first three observations?

✅ Correct Option: 2

The five observations are $x + 1$ , $x + 2$ , $x + 3$ , $x + 4$ , and $x + 5$ .

Their mean is 15.

$\text{Mean} = \dfrac{\text{Sum of all observations}}{\text{Number of observations}}$

$15 = \dfrac{(x+1) + (x+2) + (x+3) + (x+4) + (x+5)}{5}$

$15 = \dfrac{5x + 15}{5}$

$75 = 5x + 15$

$60 = 5x$

$x = 12$

The first three observations are:

$x + 1 = 12 + 1 = 13$

$x + 2 = 12 + 2 = 14$

$x + 3 = 12 + 3 = 15$

$\text{Mean of first three observations} = \dfrac{13 + 14 + 15}{3}$

$= \dfrac{42}{3}$

$= 14$

Therefore, the mean of the first three observations is $14$ .

2026: 29 May Shift 2

Salma bought 65 books for ₹ 1050 from one shop and 50 books for ₹ 1020 from another. What is the mean price she paid per book?

2022: 6 Aug Shift 1

The average of 3 even consecutive integers is 12. What is their product?

2022: 6 Aug Shift 1

The sum of the ages of 5 children born at intervals of 3 years each is 50 years. What is the age of the youngest child?

2026: 18 May Shift 2

The mean of 5 numbers is 15. If one more number is included, the mean of the 6 numbers becomes 17. Find the included number.

2023: 19 June Shift 1

What is the mode of the following data ?

4, 6, 5, 9, 3, 2, 7, 7, 6, 5, 4, 9, 10, 10, 3, 4, 7, 6, 9, 9

2025: 20 May Shift 2

The age distribution of 40 children is as follows

Age (in yr.)	5 - 6	6 - 7	7 - 8	8 - 9	9 - 10	10 - 11
No. of children	4	7	9	12	6	2

Consider the following statements in respect of the above frequency distribution.

(A) The median of the age distribution is 7 yr.

(B) 70% of the children are in the age group 6-9 yr.

Which of the above statements are true?

Choose the correct answer from the options given below:

Solution