Question

Fifteen seventh graders were randomly selected to see how many pushups in a row they could do. Their data are shown. a. b. 45, 40, 36, 38, 42, 48, 40, 40, 70, 45, 42, 43, 48, 36

Determine the mean of this data set.
Determine the median of this data set.

Answer 1

Answer: Median = 42

Mean = 43.8

Explanation:

When we have a data set of n points {x₁, x₂, ..., xₙ}

The mean is written as:

(x₁ + ... + xₙ)/N

And the median will be the value in the middle of the data set.

So first, let's write our data set in order, from least to greatest.

{36, 36, 38, 40, 40, 40, 42, 42, 43, 45, 45, 48, 48, 70}

So we have 14 values.

The middle value will be at:

(n + 1)/2

(14 + 1)/2 = 7.5

Now, counting from the left, we have that the 7.5th value is 42. (the 7th value is 42, and the 8th value is 42)

So the median is 42.

Now the mean:

M = (36 + 36 +38 +40+40+40+ 42 +42 + 43 + 45 + 45 + 48 + 48 + 70)/14

M = 43.8