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Seven numbers out of a set of nine numbers are 16, 17, 19, 19, 21, 21, and 25. If the mode of the nine numbers is 19 and the mean is 20, what are the other two numbers?

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Answer :

To find the other two numbers in the set, we need to determine the missing numbers that satisfy the given conditions.

The mode of a set of numbers is the value(s) that appear(s) most frequently. In this case, the mode is given as 19, which means that 19 appears more times than any other number in the set.

The mean of a set of numbers is calculated by summing all the numbers and dividing by the total count. In this case, the mean is given as 20.

Given that the seven numbers provided are 16, 17, 19, 19, 21, 21, and 25, we can calculate the sum of these numbers:

16 + 17 + 19 + 19 + 21 + 21 + 25 = 138

To find the sum of all nine numbers in the set, we can use the mean formula:

Mean = (Sum of all numbers) / (Total count)

20 = (138 + x + y) / 9

Simplifying the equation, we have:

180 = 138 + x + y

x + y = 42

Now, since the mode is 19, we know that either x or y (or both) must be 19. Since the mode appears twice, we can assign 19 to both x and y:

x = 19

y = 19

Therefore, the other two numbers in the set are both 19.

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