Differentiate the three measures of central tendency: ungrouped data.

Question

Glenn Cooper · Accepted Answer

Step 1
The three measures of central tendency are :
1) Mean
2) Median
3) Mode
MEAN
- The arithmetic mean is the most common measure of central tendency.
- It is calculated by summing/adding all the terms dividing by the number of terms.
- It is also known as average of data.

\overset{―}{X} = \frac{\sum X}{N}

where

\overset{―}{X} \to

Mean of the data

\sum X \to

Summation of all terms

N \to

Number of terms
Step 2
MEDIAN

\to

The median is the middle value of the ordered data.
Steps to finding the median for a set of data :
1) Arrange the data in increasing order i.e. smallest to largest
2) Find the location of the median in the ordered data by

\frac{n + 1}{2}

, where n is the sample size.
3) The value that represents the location found in above step is the median.
Formula
If n is odd, then Median is

{(\frac{n + 1}{2})}^{t h}

observation.
If n is even, then Median is

\frac{1}{2} [{(\frac{n}{2})}^{t h} + {(\frac{n + 1}{2})}^{t h}]

.
Step 3
MODE
- The mode is the value that occurs most often in the data.
- It is important that there may be more than one mode and no mode in the data set.
Example :
Given dataset : 10, 12, 18, 12, 7, 52, 16, 12
Solution: In given data set 12 occurs most i.e. 3 times.
Hence 12 is the mode of the given data.

Differentiate the three measures of central tendency: ungrouped data.

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