MEASURE OF CENTRAL TENDENCY ( MEAN) FOR STATISTICS O LEVEL/IGCSE

INTRODUCTION

The tendency of the observations to cluster in the central part of the data set is called central tendency and the summary value as a measure of central tendency.

TYPES OF AVERAGES

MEAN

It is defined as the value obtained by dividing the sum of all the observations by their number. Formula given below

Mean=sum of all the observations / number of the observations

Or

Mean = ∑xi/n (for single set of observations)

Mean = ∑ƒx / ∑ƒ (for frequency-distributions)

Example: find the mean of the following set of numbers.(single set of observation)

146,164,157,171,167,182.

Solution

Mean=∑xi/n

Mean = (146+164+157+171+167+182)/6

Mean=6

Example:( for frequency distribution)

x	f (frequency)	f(x) multiply
0	5	0
1	10	10
2	5	10
3	10	30
4	5	20
10	2	20
Sum:	37	90

Step 1. Multiply ƒ(x)

Step 2. Sum ƒ, Sum ƒ(x)

Step 3:∑ƒx/∑ƒ : 90/37=2.43

ADVANTAGES OF MEAN

1. It is based on all the observation in the data.
2. It is easy to calculate and comprehend.
3. It is determined for almost every kind of data.
4. It is the best measure to compare two or more series of data.

DISADVANTAGES OF MEAN

1. It is greatly affected by extreme values in the data.
2. It cannot determine for the quantitative data.
3. It cannot be calculated if all the values are not known.

USES

• A common man uses mean for calculating average results.
• It is extensively used in practical statistics.
• Estimates are always obtained by mean.
• Business man uses it to find the cost or profit per unit of article.