CLASS XI
Subject- mathematics
TOPIC:- MEASURES OF DISPERSION
Teacher oriented
Statistics is derived from Latin word status which means a political state. This suggests
that statistics is an old as human civilization. The scope of statistics includes collection of
numerical data purloining to almost every field, calculation of percentage, exports and
imports, birth and deaths, marriage and divorces etc.
It is useful in business, economics,
sociology, biology, psychology, education, physics, chemistry, agriculture and related
fields.
The method of finding a representative value for the given data. This value is
called the measure of central tendency Mean, Median and Mode are three measures of
central tendency. A Measure of central tendency gives us a rough idea where data points
are centered. But in order to make better interpretation from the data we should also have
an idea how the data are scattered or how much they bunched around a measures of
central tendency.
Student oriented
Students are well conversant with the methods of collection of a data, grouped data and
graphical representation of data. The terms frequency distribution, discrete and
continuous distributions, class interval, class maxe and range.
Students have an idea about
measures of central tendency like Mean, Median and Mode.
Concept details
The various measures of the central value i.e. Mean, Median and Mode give us a single
value which represents the whole data. But these measures cannot adequately describe a
set of observations, so it is necessary to describe some variation of the observations.
The
various measures of dispersion are:i) Range.
ii) Mean deviation and standard deviations.
iii) Quantity deviation.
i) Range: It is the difference between the minimum and maximum observations of data
ii) Mean deviation: The mean deviation is the observations from the mean or median or
mode of the data.
Mean deviation for ungrouped data
M.D. =1⁄n ∑ xi -A
Therefore,
M.D. x (bar)=1⁄n ∑xi-A
And
where x(bar)=mean
M.D (M) =1/n ∑xi-M
where M=median
Mean deviation for grouped data
M.D. =1/N ∑fi xi-A
Thus,
M.D. (x (bar)) =1/N ∑fi 
And
M.D. (M) =1/N ∑fi 
where ∑fi=N
xi -x (bar)
xi -M
where x (bar) =Mean
where M=Median
The number M.D. (about mean) is called the coefficient of mean deviation (about Mean)
Mean
And the number M.D (about median) is called the mean deviation (about Median)
Median
Activity
Diagnosis (Instant diagnosis)
Diagnosis (Formative diagnosis)
Levelwise Assisment
1) Find the range of the data: 35, 50, 48, 69, 39, 43, 72, 56, and 68.
2) Find the mean of first n natural number.
3) If the S.D. of the item
x1, x2, x3,…….xn is . Write the S.D. of the item an1,
an2, an3, …….ann.
4) Find mean deviation about median: 12, 5, 14, 6, 11, 13, 17, 8, and 10.
5) Find Mean deviation about median:-
Class
0-10 10-20 20-30 30-40 40-50 50-60
Frequency 6
8
11
5
5
2