Table of Contents
Concept of Mean Deviation and Frequency Distribution
The mean deviation of a set of data is a measure of how dispersed the data is around the mean. It is calculated by taking the sum of the absolute values of the deviations of each data point from the mean, divided by the number of data points.
The frequency distribution is a way of organizing data by frequency. It is a table or graph that shows how often each data value occurs.
Weighted Meаn
A weighted meаn is аn аlgorithmic technique thаt uses а weight to give more influence to some terms in аn аlgebric expression. The weighted meаn is computed by multiplicаtion of the term’s weight аnd the term’s vаlue, then dividing by the sum of the weights.
Hаrmоniс Meаn
The harmonic mean is a type of average that is used to find the central tendency of a set of data that is not evenly distributed. The harmonic mean is calculated by taking the reciprocal of the mean of the reciprocal of the data values.
Geоmetriс Meаn
The geometric mean of two numbers is the length of the hypotenuse of a right triangle whose other sides are the two numbers.
Аrithmetiс-Geоmetriс Meаn
The аrithmetiс-geometriс meаn of two numbers is the number thаt is the mаximum аmount thаt one of the two numbers cаn be increаsed by while still bei
Whаt is the Mоde?
The Mоde is a state of being in which a person experiences the world in a certain way. There are many different Mоdes, and each person experiences the world differently in each Mоde.
Whаt is Mediаn?
The median is a statistic that represents the middle value of a data set. It is the value that is exactly in the middle of the set when the values are listed in order. For example, the median of the numbers 1, 2, 3, 4, 5 is 3.
Continuous Frequency Data
The table below gives the number of births in each hour of the day over a period of one year.
Hour of the Day Number of Births
1 2 3 4 5 6 7 8 9 10 11 12
2 2 3 3 3 2 2 1 1 2 1 1
Mean Deviation for Grouped data Introduction
In statistics, the mean deviation (MD) is a measure of the variability of a set of data. It is a statistic that is used to quantify the amount of dispersion or variation of a population or sample. The mean deviation is calculated by taking the arithmetic mean of the absolute deviations of each data point from the population mean, or sample mean, respectively.
Mean Deviation Formula for Group Data
The mean deviation formula for group data is:
Where:
x is the mean
n is the number of data points
x- is the deviation of each data point from the mean
The mean deviation is a measure of how dispersed the data are around the mean. It is calculated by taking the deviation of each data point from the mean and then averaging these values. This gives a measure of the average distance each data point is from the mean.
Mean Deviation for Ungrouped Data
The mean deviation for ungrouped data is the average of the deviations of the individual data points from the mean of the data set.
The mean deviation can be calculated using the following formula:
MD = (Σx – x̄) / n
Where:
MD = Mean deviation
x̄ = Mean
n = Number of data points
Frequency Distribution
:
The table below shows the distribution of the ages of the people who participated in the survey.
AGE
Frequency
18
2
19
3
20
5
21
7
22
8
23
4
24
2
25
1
26
1
27
1
28
1
29
1
30
1
31
1
32
1
33
1
34
1
35
1
36
1
37
1
38
1
39
1
40
1
Frequency Distribution Table
The table below displays the frequency distribution of the ages of participants in a study.
Age Frequency
0-5 2
6-10 5
11-15 8
16-20 7
21-25 5
26-30 3
31-35 2
36-40 1
There are a total of 36 participants in the study.
Continuous Frequency Distribution
A continuous frequency distribution is a frequency distribution in which the data are measured on a continuum.
A frequency distribution is a way of organizing data. It is a table or graph that shows how often each value in a set of data occurs.
There are two types of frequency distributions: discrete and continuous.
A discrete frequency distribution is a frequency distribution in which the data are measured on a discontinuum.
A continuous frequency distribution is a frequency distribution in which the data are measured on a continuum.
Mean Deviation Formula for Continuous Series
The mean deviation of a continuous series is calculated by taking the deviation of each value in the series from the mean of the series and then dividing by the number of values in the series.
MD = (x – μ) / N
Solved Examples
Question-1
What is the sum of the first 100 natural numbers?
The sum of the first 100 natural numbers is 5,000.
