Mean Median Mode Formulas - How Calculate Mean Median Mode
Mean, Median, and Mode are the three of the most commonly used averages in statistics. These three can also be defined as the different measures of the centre of a numerical dataset. Identification of the central position of any data set while describing a set of data is known as the measure of central tendency. Every day we come across different kinds of data in newspapers, articles, in our bank statements, mobile, electricity bills, etc. Is it possible to figure out some important features of the data by considering only a few representatives of the data? Yes, This is possible by using measures of central tendency or averages, namely mean, median, and mode.
Mean
Mean is the arithmetic average of the given data set. Mean is calculated by adding the sum of values in a data set and dividing it by the number of observations in the data set.
x = ∑x / N
Where,
∑ is the summation.
X is the observations.
N is the number of observations.
The mean is classified into three. They are,
Arithmetic Mean
Geometric Mean
Harmonic Mean
Median
It is the middle point of a set of observations when the numbers are in ascending or descending order.
When the number of observations (n) in the set is odd, the median formula is
Median = [(n + 1) / 2]
When the number of observations (n) in the set is even, the median formula is
Median = [(n / 2) + (n / 2 + 1)]/2
Mode
Mode is the most often occurring value in a data set. The difference between the highest and lowest values in a data set is called the range.
Mode = 1 + [(fₘ − f₁) / (2fₘ − f₁ − f₂)] × h
Where,
l is the lesser limit of the class
fₘ is the frequency possessed by the modal class
f₁ is the frequency possessed by the class before the modal class
f₂ is the frequency possessed by the class after the modal class
h is the width of the class
Relationship Between Mean, Median and Mode
The Mean, Mode and Median are related as
2 Mean + Mode = 3 Median
For Example,
If, Mode = 65 and Median = 61.6, Mean= ?
In this case, where mode and median are given and mean should be found.
Use (2 Mean + Mode = 3 Median) formula
2 Mean = (3 × 61.6) – 65
2 Mean = 119.8
Mean = 119.8 / 2
Mean = 59.9
FAQs on Mean Median Mode Formula
1. What is mean and explain with examples.
The mean of a series of data is the value equal to the sum of the values of all the observations divided by the number of observations. It is the most commonly used quantifier of central tendency. Also, it is very easy to measure.
x̅=∑x/ N
Here,
∑ represents the summation
X represents scores
N represents a number of scores.
x̅ = Sum of all the values of the observations/ No.of observations
Example: what is the mean of 2, 9 and 7?
Add all the three numbers: 2 + 9 + 7 = 18
Divide by how many numbers (i.e. we added all the 3 numbers): 18 ÷ 3 = 6.
So the mean is 6.
2. What is the median?
Median is the central or the middle value of a data series. In other words, it is the mid-value of a series that divides it into two parts such that one half of the series has the values greater than the Median whereas the other half has values lower than the Median. For the calculation of Median, we need to arrange the data series either in ascending order or descending order.
Individual Series
When the number of observations is odd
M = Size of (N+1)th/ 2 term.
Where N is the number of observations.
3. What is the mode?
Mode refers to the value that occurs a most or the maximum number of times in a data series.
Mode formula
Individual Series:
We find the mode of an individual series by simply inspecting it and finding the item that occurs the maximum number of times.
Discrete Series:
The Mode of a discrete series is the value of the item that has the highest frequency.
Frequency Distribution or Continuous Series:
Firstly, we need to find out the Modal class. Modal class is one of the class with the highest frequency.
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5. Given the set of observations, x = (1, 3, 5, 7, 9), find the mean?
Use the formula,
Mean, x = ∑x / N
x = (1 + 3 + 5 + 7 + 9) / 5
x = 25 / 5
x = 5.
6. Given the set of observations, x = (10, 20, 30, 40, 50), find median?
Check the number of observations, whether it has odd or even number of terms.
Arrange them in Ascending order
For odd number of observation use formula,
Median = [(n + 1)/2]
= [(5 + 1) / 2]
= 6/2
= 3
Therefore the value which is at the 3rd position in the given set of observation is the median. 30 is the median of the given set.
7. Given the set of observations, x = {21, 34, 43, 21, 34, 56, 7, 9, 0}, find the mode?
In this set of observations look for the value which is repeated the most.
The value 21 and 34 is repeated twice, therefore there are two modes for this set.
8. The age of 9 persons are given, x= (13, 18, 13, 14, 13, 16, 14, 21, 13), find the mean median and mode of the person with respect to their age?
Mean,
x = ∑x / N
= (13 + 18 + 13 + 14 + 13 + 16 + 14 + 21+ 13) / 9
= 135 / 9
x = 15
Median,
Arranging the values in ascending order, and check whether the number of observation is odd or even
(13, 13, 13, 13, 14, 14, 16, 18, 21)
For odd number of observation use formula,
Median = [(n+1) / 2]
= [(9 + 1) / 2]
= 10/2
= 5.
The value at the 5th position in the set of observations is the median. Therefore, 14 is the median.
Mode
In this set of observations look for the value which is repeated the most.
The value 13 is repeated the most. Therefore, 13 is the mode of the given set of observations.
9. An organization consists of 5 members- 4 Workers and 1 supervisor. The salary of a supervisor is 4000, the salary of a worker is 1000. Calculate the mean and median?
x= (1000, 1000, 1000, 1000, 4000)
Mean, x = ∑x / N
= 8000 / 5
x = 1600
Therefore, 1600 is the mean salary of the organization.
Median,
Arrange the values in ascending order
Median = [(n+1) / 2]
= (5+1)/2
= 6/2
Median = 3
The value at the third position is the median. Therefore 1000 is the median value.