**Statistical Functions**

**Statistical functions** normally refer to the (arithmetic) mean or the average, the median, the mode, the range of value in a set, the variance, and the standard deviation.

On this page we give 3 examples of the mean and the median.

**To practice more of these types of problems, click** here.

**Example 1)**

If 8 boys in a gym class are 5 1/4 feet tall, and 4 boys are 6 feet tall, what is the average height of these boys?

A. 5 3/4 feet

B. 5 1/2 feet

C. 5 3/8 feet

D. 5 7/8 feet

E. 5 3/5 feet

**Explanation:** The average is the mean, and the mean is

((8 × 5 1/4 ) + ( 4 × 6))/12 = (42 + 24)/12 = 66/12 = 5 1/2

**The correct answer is B.**

**Example 2)**

If y is the mean and x the median of the numbers, m+4, m-5, m-6, m+2, m+5, then what is x – y?

A. 0

B. 1

C. 2

D. 2m

E. 2m + 2

**Explanation:** First, we put the numbers in ascending order.

m-6, m-5, m+2, m+4, m+5

Then the median is the middle value of this list: x = m+2.

The mean is the average of these 5 numbers: y = (m-6 + m-5 + m+2 + m+4 + m+5)/5 = (5m – 11 + 11)/5 = 5m/5 = m.

So x – y = m + 2 – m = 2.

**Answer C is correct.**

Notice that since we’re looking for x – y then the values for m subtract out, and we’re left with a literal number, 2. If instead we added x and y, we would get

x + y = m + 2 + m = 2m + 2, which is answer E.

**Example 3)**

From 20 summer lawn mowing jobs Teri averaged $18 per job. If she averaged only $15 on 8 of the jobs, what did she average on the other 12?

A. $22

B. $20

C. $21

D. $24

E. $19

**Explanation:** Teri received total pay on the 20 jobs of 20 × 18 = 360. She got 15 × 8 = 120 on 8 of the jobs, so her average on the other 12 was

(360 – 120)/12 = 240/12 = 20

**So B is the correct answer.**

**To practice more of these types of problems, click** here.