Statistic

Determining the Mean of a Given Set of Data

The mean sometimes called the arithmetic mean is the most common average.

If there are n numbers in a set, then

Mean = sum of numbers in a setn

When the set of data is tabulated, we use the formula: ƩfxƩf

Example 1:

In a class test, a student had the following marks:

13, 17, 18, 8, 10. What is the average mark?

Solution:

Average (mean) = sum of numbers in a setn

= 13+17+18+8+105665

= 665

= 13.2

Example 2: A hockey team has played eight games and has a mean score of 3.5 goals per game. How many goals has the team scores?

Solution:

Mean score = number of goalsnumber of games

3.5 = number of goals8

Multiply both sides by 8

3.5 × 8 = total number of goals

28 = total number of goals

Median

Median simply refers to the middle item when the set of data is arranged in the right order. When the number of item is odd, the median will be a single item. When the number of items is even, two items will fall in the middle. In such case, the sum of the two items is obtained and divided by two.

Example 1:

Find the median of these numbers:

13, 15, 14, 12, 13, 15, 16, 10, 12, 14

Solution:                     

Arrange the numbers in order of magnitude starting with the smallest value:

Add the two middle numbers and divide the result by 2

Median = sum of the two middle numbers2

= 13+142

= 1312

Example 2:

Find the median of 8.4, 7.8, 6.2, 13.4, 12.6, 10.5

Solution:

Arrange the set of numbers in order of size.

6.2, 7.8, 8.4, 10.5, 12.6, 13.4

There are 6 numbers. The median is the mean of the 3^rd and 4^th numbers.

Median = 8.4+10.52

= 18.92

= 9.45

Mode

Mode is defined as the most frequent score in a data set. It represents the highest bar in a bar chart or histogram. Therefore, the mode is sometimes regarded as being the most popular option. Below is an example of mode:

Example 1:

Find the mode of the numbers 6, 6, 8, 9, 9, 9, 10

Solution:

The most occurred item is 9, hence, the mode is 9.

Example 2:

The chart shows the different means by which students of ABC School come to school. Find the modal means of transportation.

It is clear from the chart above that the most common form of transport, in this particular data set, is the bus. However, one of the problems with the mode is that it is not unique, so when a set of data has two most occurring items, we pick both items. Such frequency is called bi-modal frequency.

PRACTICE EXERCISES

1. Find the median of these numbers:

(a) 5, 8.6, 4.8, 10.5, 6.8, 7.5, 8.2

(b) 50%, 55%, 60%, 70%, 65%

(c) -3⁰C, -2⁰C, 0⁰C, 4⁰C, -4⁰C, -1⁰C, 2⁰C, -2⁰C, 1⁰C, -1⁰

(d) 2, 8, 9, 12, 7, 5, 6, 4, 5, 10, 11, 3, 6.

2. The table below gives the ages and frequencies of girls in a choir.

. The table below gives the ages and frequencies of girls in a choir.

Find the

(a) number of girls in the choir;

(b) modal and median ages of the choir;

(c) mean age of the choir.

2. The table below shows the marks of students in a mathematics test.

Find the

(a) number of students who took part in the test;

(b) number of students who scored at most 6;

(c) median mark;

(d) modal mark.