CENTRAL TENDENCY

A measure of central tendency represents mid-value or the most occurring value a large collection of numerical data. It is of significance because it depicts the nature or characteristics of the entire data.

The mean is the sum of observations divided by the count of observations.

Example: Consider the dataset: 34, 76, 98, 80, 15, 44, 54

Mean = 401/7

Mean = 57.3

The median is the middle value of a set of numbers arranged in ascending or descending order.

ODD NUMBER OF DATA POINTS

Example: Consider the dataset: 25, 63, 95, 85, 12, 32, 41

Solution

In the above dataset, there are 7 data points, so firstly, arrange the data points in ascending order (lowest to greatest), i.e.,

12, 25, 32, 41, 63, 85, 95

Median = ((n+1)/2)^th

Median = ((7+1)/2)^th

Median = 4^th value

Hence, the median is 41.

EVEN NUMBER OF DATA POINTS

Example: Consider the dataset: 27, 60, 98, 88, 18, 78

In the above dataset, there are 6 data points, so firstly, arrange the data points in ascending order (lowest to greatest), i.e.,

18, 27, 60, 78, 88, 98

Median = [(n/2)^th term + ((n/2) + 1)^th term] / 2

Median = [(6/2)^th term + ((6/2) + 1)^th term] / 2

Median = [(3^th term + 4^th term] / 2

Median = 98+88/2 = 93

Hence, the median is 93.

The mode is the most frequently occurring value in a dataset.

Example: Consider the dataset: 27, 60, 88, 88, 88, 78

88 is the most frequently occurring item.

Mode is 88