Frequent And Central Math

Frequent And Central Math

The world population just crossed 7 billion! Is it wonderful or are you plagued by the fact? While a number of countries claim the credit of producing the 7 billionth child of the world, it is not what I am interested in. I have always been interested by the different characteristics, cultures etc. of the billions of people walking the earth with me.

But the research is not an easy task because the population of a particular place is subject to constant change and mobility. For this reason researchers take refuge in the study of central tendencies and frequency distribution.

Let us take a look at them.

Remember that the various samples of data chosen are random samples so that every element of the nature of the data is equally likely to be selected.

Frequency distribution

After a sample has been chosen, it must be organized so that the conclusions are more easily drawn. Usually the data is organized in groups of equal intervals.

An example will clear the matter.

Mr. David gave a Science test to his class of 20 students. Below are the marks each of them scored. Arrange them in a frequency table.

100, 93, 91, 79, 89, 90, 80, 77, 78, 95, 86, 76, 83, 88, 80, 76, 84, 85, 87, 79

Notice that the highest is 100 and the lowest is 76. We can easily group the given data in intervals of 5. This is convenient as it gives an interval for each number in the list and results in five equal intervals. First tally the number of students falling into each interval and then total the tallies as shown.

 Marks Tally Frequency 76 – 80 8 81 – 85 3 86 – 90 5 91 – 95 3 96 - 100 1

Measure of central tendency

The three types of the measure of central tendency:

Mode

- Mode is the value that appears most frequently in a set of data. If every value in a set of data occurs only once then there is no mode. If, in a set of data, two numbers occur most frequently and for the same number of times, it is called bimodal i.e. two mode.

Example: Find the mode of the given data set, which shows the heights (in inches) of 10 students in Mr. Ben's class

Solution:

Heights = 67, 48, 32, 59, 61, 55, 61, 65, 40, and 75

Mode is the data item that appears most often in the data set.

Here 61 occur most often.

Median

– It is a type of Average that is found by:

• First arrange the given numbers in order.
• Then select the one in the middle.
• If there are an odd number of items in the number set, the median is the center term.

For example: Find the median of 17, 14 and 26

Solution:

1. Arrange the numbers in order: 14, 17, 26

2. 17 is the center term. So, 17 is the median of the given set of numbers

• If there is an even number of items, then add the two middle terms and divide by 2.

For example: Find the median of 10, 13, 5 and 7

Solution:

1 Arrange the numbers in order: 5, 7, 10, 13
2. 7 and 10 are the two middle terms,

so 7 + 10 = 17
17 ÷2 = 8.5

Mean – It is simply the sum of the numbers in the data set, divided by the number of items in the set.

This is also called average.

Example: Eric’s hobby is to collect coins. If he has collected 56, 96, 118, 109, 86, 77, 98, and 95 coins so far, find the mean of the data.

Solution:

Number of coins = 56, 96, 118, 109, 86, 77, 98, and 95.

Sum = 56 + 96 + 118 + 109 + 86 + 77 + 98 + 95

= 735

Number of the data values = 8

= 91.875
= 92 (rounding off)

So did you see how with the help of central tendencies and frequency distribution you can draw conclusions about a collection of data?