Statistics:
Statistics may be defined as the science of collection organization,
presentation, analysis and interpretation of numerical data.
Population: Population means aggregate of elements
possessing certain characteristics of interest in any particular investigation
or inquiry.
Sample: A sample is a part of population which
represents the population.
Variable: The measurement of elements of a population
having certain characteristics that may vary from element to element either in
magnitude or in quality.
Classification
of variable: There are 2 types.
- Qualitative variable
- Quantitative variable
Qualitative variable: The variable which can’t be measured but can
be categoried is called qualitative variable. I.e. Hair color, merit of
student.
Quantitative variable: The variable which can be measured is called
Quantitative variable.
I.e. height of student,
No. of children in families.
Types of
Quantitative: There are 2 types of
Quantitative variable
- Discrete variable
- Continuous variable
Discrete variable: When a variable can assume only isolated or
integral values. Then it is called Discrete variable. i. e. No. of children in
families.
Continuous: A variable is said to be continuous if it
assumes any value either in integral or factoral within a certain range.
Frequency: The number of observation or values falling
into each group or class is called frequency. The frequency shows how many
times a fasticular value or observation is repeated.
Frequency Distribution: A set of classes together with the
frequencies occurrence of values in each class in a given set of data presented
in tabular form a referred to as a frequency distribution.
Types of frequency
distribution:
There are 2 types of frequency distribution.
- Discrete frequency distribution
- Continuous frequency distribution
General representation
of frequency distribution:
- Bar diagram
- Histogram
- Frequency polygon
- Cumulative frequency polygon (Ogive)
- Pichart…………….etc.
Bar diagram:
This diagram is drawn
by eracting a series of blocks of equal width. But with heights proportional to
the value of corresponding to different time period or categories etc.
Drawn
a Bar Diagram from the following data:
Ponds: A
B C D
No. of fishes:
150 300 450 500
Figure:
Bar Diagram
Histogram: In this case magnitude of the class interval
is plotted along horizontal axis and the frequencies are in the vertical axis.
The height of the rectangles will be proportional to the frequencies of the
class interval.
To draw a histogram
from the following frequency distribution:
Marks:
0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90
No. of student: 0 2 3 7 12
10 2 1 5
 |
| Figure: Histogram |
Frequency polygon:
In frequency polygon the midvalues of the class intervals are represented along
X-axis and the frequencies along Y-axis. The class frequencies are plotted
against the mid values of the respective class intervals. These points are jointed
by straight line one after another. The first and the last points are then
brought down at each end to the X-axis by joining it to the midvalues of the
next class intervals of zero frequencies. The polygon construction of a
frequency polygon from the following data:
C.T. Midvalue Frequency
24.5-29.5 27 13
29.5-34.5 32 15
34.5-39.5 37 15
39.5-44.5 42 16
44.5-49.5 47 22
49.5-54.5 52 17
54.5-59.5 57 02
Cumulative
frequency polygon: In cumulative frequency polygon the
upper limit of the class interval are represented in the X-axis and the
cumulative frequency are represented in the Y-axis. A free hand curve to smooth
a cumulative frequency polygon is called ogive.
C.I. Frequency
Cumulative frequency
24.5-29.5 13 13
29.5-34.5 15 28
34.5-39.5 15 43
39.5-44.5 16 59
44.5-49.5 22 81
49.5-54.5 7 98
54.5-59.5 2 100
Pie chart:
Pie chart is used when
relationship of the parts is shown to one another and to the total. A circle
consists of 360
. The total values of the series are
equated 360
and then the angles corresponding to the
compound parts are calculated.
As for example:
Continent Area (Miles)
Asia 18.30
Africa 11.70
Europe
1.90
North
America 9.4
South
America 6.9
Australia
3.3
The angle subtended at
the circle by Asia will be
=
127.922
Frequency Curve:
If the numbers of observation are large and the length of class interval can be
reduced. The frequency polygon will provide a curve usually called frequency
curve.
Types of frequency curve:
v Symmetrical
curve
v Moderately
asymmetrical or skew curve
v Extremely
asymmetrical or J-shaped curve
v U-shaped
curve
Symmetrical curve: A
frequency curve is said to be symmetrical if the frequency at the point is
maximum and the rate of decrease from the peak is same in both sides. If the
curve can be folded along a vertical line the two halves will coincide.
Moderately asymmetrical: A
frequency is said to be skew frequency curve if it is lacking of symmetry. In
this curve the tail of the curve one is longer than the other. If the longer
tail occurs to the right sides, the curve is said to be positively skew curve,
otherwise it is negatively skew curve.
Extremely asymmetrical:
A
frequency curve is said to be J-shaped if the maximum frequency occurs at one
end of the distribution. If the maximum frequency occurs at the left end then
it gives a positively J-shaped curve, otherwise it is called negatively
J-shaped curve.
U-shaped curve:
A frequency curve is said to be
U-shaped if the maximum frequency occurs at both and of the distribution while
the minimum at the middle. This curve looks like a letter U.
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