statistics class 11

Statistics
BY
SHIVANG BANSAL (XI-B)
Statistics is derived from the Latin word ‘status’ which means a political state. This suggests
that statistics is as old as human civilization.

INDEX:
 INTRODUCTION
 DATA
 MEASURES OF DISPERSION
 MEAN DEVIATION OF GROUPED DATA
 MEAN DEVIATION OF UNGROUPED DATA
 STANDARD DEVIATION AND VARIANCE
 FREQUENCY POLYGON

INTRODUCTION
 We know that statistics deals with data collected with specific purposes. We can make
decisions about the data by analyzing and interpreting it.
 In earlier classes, we have studied methods of representing data graphically and in tabular
form. This representation reveals certain characteristics of the data.
 We have studied the methods of finding a representative value for the given data. This
value is called the measure of central tendency.
 Recall mean(arithmetic 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 are bunched around a measure of central tendency.

DATA
 Data can be defined as a systematic record of a particular quantity. It is the different
values of that quantity represented together in a set. It is a collection of facts and figures
to be used for a specific purpose such as a survey or analysis.
Types of Data
 Qualitative Data: They represent some characteristics or attributes. They depict
descriptions that may be observed but cannot be computed or calculated. For example,
data on attributes such as intelligence, honesty, wisdom, cleanliness, and creativity
collected using the students of your class a sample would be classified as qualitative.
They are more exploratory than conclusive in nature.
 Quantitative Data: These can be measured and not simply observed. They can be
numerically represented and calculations can be performed on them. For example, data
on the number of students playing different sports from your class gives an estimate of
how many of the total students play which sport. This information is numerical and can
be classified as quantitative.

Measures of Dispersion
The dispersion or scatter in data is measured on the basis of types of measure of central
tendency , used there.
There are following measures of dispersion:
 Range: The limits between which something can vary.
 Quartile deviation: One half of the difference obtained by subtracting the first quartile
from the third quartile in a frequency distribution.
 Mean deviation: The mean of the absolute values of the numerical differences between
the numbers of set (such as statistical data) and their mean or median.
 Standard deviation: The standard deviation is a measure of how spread out numbers are.
Its symbol is σ(the greek letter sigma).

Mean Deviation for Grouped Data
 Discrete frequency distribution : Let the given data consist of n distinct values x1, x2, x3,
….,xn occurring with frequencies f1, f2, f3,….,fn respectively. This data can be represented in
the tabular form as given below and is called discrete frequency table:
x : x1 x2 x3 … xn
f : f1 f2 f3 … fn
 Continuous frequency distribution: A continuous frequency distribution is a series in which
the data are classified into different class intervals without gaps along with their respective
frequencies.
For example, marks obtained by 100 students are presented in continuous frequency
distribution as follows
Marks obtained 0-10 10-20 20-30 30-40 40-50 50-60
No. of students 12 18 27 20 17 6

Mean Deviation for Ungrouped Data
Let n observations be x1, x2, x3 …,xn. The following steps are involved in the calculation of mean
deviation about mean or median :
 Step 1: Calculate the measure of central tendency about which we are to find the mean
deviation. Let it be ‘a’.
 Step 2: Find the deviation of each x1 from a.
 Step 3: find the absolute values of the deviations i.e., drop the (-) sign if it is there.
 Step 4: Find the mean of the absolute values of the deviations. This mean is the mean
deviation about a.
Mean Deviation=[ ∑|X – a|]÷n
Here, ∑|X-a| = The summation of the deviations for values from ‘a’
n= The number of observations

Standard Deviation and Variance
 Standard deviation is the most important tool for dispersion measurement in a
distribution. Technically, the standard deviation is the square root of the arithmetic mean
of the squares of deviations of observations from their mean value. It is generally denoted
by sigma i.e. σ.
Standard Deviation (σ)= √[∑D²/N]
Here, D= Deviation of an item relative to mean . N= The number of observations
 Although standard deviation is the most important tool to measure dispersion, it is
essential to know that it is derived from the variance. Variance uses the square of
deviations and is better than mean deviation. However, since variance is based on the
squares, its unit is the square of the unit of items and mean in the series.
Variance= ( Standard deviation)²= σ×σ

Frequency Polygon
 A frequency polygon is a graphical form of representation of data. It is used to
depict the shape of the data and to depict trends. It is usually drawn with the help
of a histogram but can be drawn without it as well. A histogram is a series
of rectangular bars with no space between them and is used to
represent frequency distributions.
 One of the basics of data organization comes from presentation of data in a
recognizable form so that it can be interpreted easily. You can organize data in the
form of tables or you can present it pictorially.
 FOR EXAMPLE,

thank you!!
“Statistics may be rightly called the science of averages and their estimates.”
–A.L BOWLEY & A.L. BODDINGTON

statistics class 11

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