Arithmetic

Central Tendency

Easy

The mean of 6 numbers is 19. If two more numbers are included, the mean of the 8 numbers becomes 23. What is the sum of the two included numbers?

✅ Correct Option: 3

The mean of 6 numbers is 19. Two more numbers are included, making 8 numbers with a mean of 23.

The mean formula is:

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

For the original 6 numbers:

$19 = \dfrac{\text{Sum of 6 numbers}}{6}$

$\text{Sum of 6 numbers} = 19 \times 6$

$\text{Sum of 6 numbers} = 114$

For all 8 numbers:

$23 = \dfrac{\text{Sum of 8 numbers}}{8}$

$\text{Sum of 8 numbers} = 23 \times 8$

$\text{Sum of 8 numbers} = 184$

The sum of the 2 new numbers is the difference between the total sum of 8 numbers and the original sum of 6 numbers:

$\text{Sum of 2 new numbers} = 184 - 114$

$\text{Sum of 2 new numbers} = 70$

Therefore, the sum of the two included numbers is $70$ .

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The mean of 6 numbers is 19. If two more numbers are included, the mean of the 8 numbers becomes 23. What is the sum of the two included numbers?

Solution

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