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.
Positional Averages: Median and Mode Management
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 91st 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