# Positional Averages: Median and Mode Management YouTube Lecture Handouts

Get unlimited access to the best preparation resource for competitive exams : get questions, notes, tests, video lectures and more- for all subjects of your exam.

## Median

Median is basically the middle value of the observations after arranging them according to the size i.e.. , either in increasing and decreasing order.

**Formula**

**For Ungrouped data**:

N + ^{th} observation

**For Grouped Data**

Where

- I = Lower limit of median Class,
- N = Number of observations,
- Cf = cumulative frequency of class preceding the median class,
- F = frequency of median class,
- H = class size (assuming class size to be equal)

### Related Positional Measures

- The median divides the series into 2 equal parts. Similarly, there are certain other measures which divide the series into equal parts.
- These are quartiles, Deciles, and percentiles. Quartiles divide the series into 4 equal parts, deciles into 10 parts whereas Percentiles divide it into 100 equal parts

#### Quartiles

- Quartiles basically divide the series in 4 equal parts and each part contains equal observations. In this way there are three quartiles.
- If a statistical series Is divided into 4 equal parts, then end value of each part is called a quartile.

#### Deciles

**Deciles**: They divide the series into 10 equal parts and there are 9 deciles expressed as D1, D2 and each one is called a decile. Here D5 is the median.- Deciles are used in finance and economics to divide data into sets for the purpose of analysis.
- For example, the data set of mutual fund portfolio or the data set of income-tax return filers can be divided for analyzing the top 10 per cent and so on.

#### Percentiles

- The percentiles divide the entire series into 100 equal parts and are generally expressed as P.
- For any series there are 99 percentiles because at the end of every part a percentile is formed.
- Percentiles indicate the percentage of scores that fall below a particular value. They tell you where a score stands relative to other scores. For example, a person with an IQ of 120 is at the 91
^{st}percentile, which indicates that their IQ is higher than 91 percent of other scores.

## Mode

- It is denoted by Mo. The value which is repeated the most numbers is basically called the Mode.
- We can have more than one mode i.e.. , a unimode, Bimode etc.

### Ungrouped Data

**Formula** = most repeated value

### Grouped Data

- Where L = lower limit of the modal class,
- H = size of the class interval (assuming all class sizes to be equal) ,
- = frequency of the modal class,
- = Frequency of the class preceding the modal class,
- = Frequency of the succeeding the modal class,

## Relations between Measures of Central Tendency

**In symmetrical distribution**:- Mean = Median = Mode

**In a positively skewed distribution**- Mean > Median > Mode

**In negatively skewed distribution**- Mean < Median < Mode

**According to Karl Pearson the relation between three can be expressed as**:- Mode = 3 Median-2 Mean

## MCQs

According to Karl Pearson, the relation between mean, median and mode is?

A. 2 mode-3 mean = median

B. Mode = 3 median-2 mean

C. Both A and B

D. None of the above

Answer: C

How many percentiles are there in a percentile?

1.88

2.100

3.99

4.9

Answer: 3

✍ Manishika