Question

The mean of five numbers in a set is 12. If the set contains a total of six numbers and the mean of all six is

14, which of the following is the sixth number?
(1) 24
(3) 32
(2) 13
(4) 18

Answer 1

Answer: 24 (choice 1)

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Step-by-step explanation:

The process of finding the arithmetic mean involves two steps

1. add up all the numbers
2. divide by n, which is the number of values in the set

The first bit of info your teacher gave you is "the mean of five numbers in a set is 12". While we don't know the actual individual values themselves, we know that they must add to some variable y. Dividing y over n gets us the mean

y/n = mean

y/5 = 12

y = 5*12

y = 60

The five values add to 60.

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The next bit of info is that "the mean of all six is 14". That allows us to say:

(sum of all 6 values)/6 = mean

(sum of all 6 values)/6 = 14

( (sum of 5 values) + (6th value) )/6 = 14

(y + x)/6 = 14

(60 + x)/6 = 14

where x is the 6th number we want to find.

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Solve for x

(60 + x)/6 = 14

60+x = 6*14

60+x = 84

x = 84-60

x = 24 so choice (1) is the answer