Question

A set of 5 numbers has an average of 50. The largest element in the set is 5 greater than 3 times the smallest element in the set. If the median of the set equals the mean, what is the largest possible value in the set

Answer 1

Answer:

5×3=15

15×3=45

therefore the largest value is 45

Answer 2

The largest possible value in the set is 92. The set has an equal mean and median. So, the set is {29, 29, 50, 50, 92}.

What are the mean and median of a set of data?

Mean:

For a set of data, the average of all the data values is said to be its mean.

Median:

When the set is arranged in ascending order, the middle term is said to be its median (if there are an odd number of data values in the set) or the average value of the two middle terms is the median (if there are an even number of data values in the set).

Calculation:

It is given that,

there are 5 numbers in the set

Mean = 50 and Median = Mean

So, Median = 50

Since there are 5 numbers in the set (odd number), the median is the third(middle) number.

Consider the first or smallest number as 's'.

Then the largest number = 3s + 5

By minimizing each term we get,

first term = s

second term = s

third term = 50

fourth term = 50

fifth term = 3s+5

If the mean is 50, then the sum of all the terms = 50 × 5 = 250

So,

s + s + 50 + 50 + 3s + 5 = 250

⇒ 5s + 105 = 250

⇒ 5s = 145

∴ s = 29

Thus, the smallest number is 29

Then, the largest number = 3s + 5 = 3 × 29 + 5 = 92

Therefore, the largest number in the given set is 92.

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