# MEASURES OF CENTRAL TENDENCY

Measures of Central Tendency is that single value that summarises the mass of data presented in a distribution, it is used mostly when describing a certain property of a population or simple.

It is those means/methods of determining the most typical value of the property in a given data.

The three types of Measures of Central Tendency are elucidated below:

## MEAN:

Arithmetic mean is the values, which each item in a distribution would get if the sum total of all the items in the distribution were equally shared among the items. The mathematical formula for calculating mean is

X =  ∑X ÷ N

where:

X stands for arithmetic mean

∑X stands for total sum of item

N stands for the number of items.

Example: Given these numbers – 2, 4, 6,8,10 as the values of items of a distribution, calculation the mean.

Solution: Now, to get the mean of the above given numbers, we sum up the total of the items and then divide by the number of the items.

i.e. (2+4+6+8+10) = 30

30 ÷ 5 = 6.

1. It serves as an instrument of comparison
2. It is the most commonly used and reliable measures of central tendency. 3. It has a stable value.
3. It is the most suitable for further statistical analysis.

1. The results could be distorted.
2. It is very difficult for it to be located by mere inspection.
3. The results can be influenced by unrepresentative values.
4. It is difficult to compute when the datas are many.

## MEDIAN

is the value or the middle item of a given distribution. In selecting the median, it is pertinent to arrange the items either in ascending or descending order of importance. But where odd numbers exist, the middle number is considered the median. For instance, given these numbers 1, 2, 3, 4, 5. To get the median, the middle number will be taken. Therefore, the median to the above is 3. But for even- number distribution, the average of the two middle numbers make up the median. E.g. 1, 3, 4,5,6,7. The median is  (4+5)÷ 2 = 9÷ 2 =4.5.

1. It can be graphically determined
2. It is easy to calculate
3. It gives a balanced value of a data
4. It is easily understood and can be used for qualitative data.

1. The formula sometimes is misleading and may not yield a correct result.
2. It cannot be easily calculated as exactly as the mean
3. Calculation of median may require re-arrangement of result could be achieved
4. It is not suitable for further statistic measures

## MODE

Is the value or number that occurs most frequently in a distribution. That is, it is the most common number, E.g. 6,4,5,6,7,8.

From the above values, the most frequently occurring number or value is 6. Therefore, the mode of the distribution given is 6.

NOTE: For group data, the formula for mode is:

Mode L1+ (D1/(D1 + D2))

Where L1 = Lower class boundary of modal class

D1 = Excess of modal frequency over Frequency of next lover class

D2 = Excess of modal frequency over Frequency of next higher class,

C = Size of modal class interval

1. It is the most popular value.
2. Extreme values have no effect on it.
3. It is simple and easy to compute.