Arithmetic

Central Tendency

Easy

The average of nine numbers is 50. The average of the first five numbers is 54 and the average of the last three numbers is 52. Find the sixth number of this set of numbers?

✅ Correct Option: 1

The average of all 9 numbers is 50.

Average $=$ Total Sum $\div$ Count of Numbers

Total Sum $=$ Average $\times$ Count of Numbers

Sum of all 9 numbers:

$50 \times 9 = 450$

The average of the first 5 numbers is 54.

Sum of first 5 numbers:

$54 \times 5 = 270$

The average of the last 3 numbers is 52.

Sum of last 3 numbers:

$52 \times 3 = 156$

Sum of all 9 numbers $=$ (First 5 numbers) $+$ (6th number) $+$ (Last 3 numbers)

$450 = 270 + \text{6th number} + 156$

$450 = 426 + \text{6th number}$

$\text{6th number} = 450 - 426$

$\text{6th number} = 24$

Therefore, the sixth number is $24$ .

2022: 23 Aug Shift 1

The average of the four consecutive odd numbers is 16. What is the third number in the descending order?

2022: 8 Aug Shift 1

The average age of group of 5 friends is 32 years. The youngest friend amongst them is 4 years old. What was the average age of the group at the time of birth of the youngest friend?

2026: 22 May Shift 2

For a certain distribution, mode and median were found to be 1000 and 1250 respectively. Find the mean of this distribution using an empirical relation.

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: 15 May Shift 1

Read the information given below carefully and answer the question that follows:

(A) If the mean of 5 numbers is 15 and then if 27 is included to the numbers, then the mean of the 6 numbers shall be 17

(B) The mean of marks of 300 students is 60, the mean of the top 100 students' marks is 80 and the mean of the last 100 students is 50, then the mean of the marks of the rest of the 100 students of the group is 60.

(C) The mean and median of 5 observations is 9 and 8 respectively, if 1 is subtracted from each observation, then the new mean and median shall be 8 and 7 respectively

Choose the correct answer from the options given below:

2026: 26 May Shift 1

The median of frequency distribution is:

Class :	0 – 25	25 – 50	50 – 75	75 – 100
Frequency :	23	32	15	12

The average of nine numbers is 50. The average of the first five numbers is 54 and the average of the last three numbers is 52. Find the sixth number of this set of numbers?

Solution

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