IMPORTANT CONSIDERATION IN THE CONSTRUCTION OF A FREQUENCY DISTRIBUTION and GRAPHICAL REPRESENTATION OF A FREQUENCY DISTRIBUTION

1. TOPIC
•IMPORTANT CONSIDERATION IN THE
CONSTRUCTION OF A FREQUENCY
DISTRIBUTION
•GRAPHICAL REPRESENTATION OF A
FREQUENCY DISTRIBUTION
PRESENTING BY,
MOHAMMED NASIH B.M

2. FREQUENCY DISTRIBUTION
• Frequency Distribution is a classification of data showing the
number of occurrences of each interval or category of a variable.
In the case of a quantitative variable the class intervals are
arranged in order of magnitude.
• A frequency distribution provides a basic ordering of data, and is
usually the first step in statistical analysis.

3. IMPORTANT CONSIDERATIONS
1. Find the range of data : The range is the difference between
the largest and smallest values.
2. Decide the approximate number of classes : Which the data
are to be grouped. There are no hard and first rules for number
of classes. Most of the cases we have 5 to 20 classes.

4. Contd..
• H.A Sturges has given a formula for determining the approximation number
of classes.
K = 1+3.322 logN
Where K = Number of classes ,
logN = logarithm ogf the total number of observations

5. Contd..
• For example :
if the total number of observation is 50, the number of classes would be
K= 1+3.322 logN
K= 1+3.322 log 50
K= 1+3.322(1.698)
K= 1+5.643
K= 6.643 That is 7 classes approximately.

6. Contd..
3. Determine the approximate class interval size : The size of class interval
is obtained by dividing the range of data by number of classes and denoted
by ‘h’ class interval size.
h = Range / Number of classes
4. Decide the starting point : The lower class limits or class boundary should
cover the smallest value in the raw data. It is a multiple of class interval.
for example : 0.5.10,15,20,25 etc. are commonly used

7. Contd..
5. Determine the remaining class limits : When the lowest class boundary
of the lowest class has been decided, then by adding the class interval size
to the lower class boundary, compute the upper class boundary. The
remaining lower and upper class limits may be determined by adding the
class interval repeatedly till the largest value of the data is observed in the
class.
6. Distribute the data into respective classes : All the observations are
marked into respective classes by using Tally Bars methods which is
suitable for tabulating the observations into respective classes. The total of
the frequency columns must be equal to the number of observations.

8. GRAPHICAL REPRESENTATION
OF FREQUENCY DISTRIBUTION

9. • The graphical representation makes visual comparison of data
easier and gives a more lasting impression than is possible by any
other means.
• Objective
1. The histogram is particularly appropriate to cases in which classes are not of equal
width.
2. The main purpose of the polygon is to find the mode of the given series. Mode
can be ascertained fairly accurately by the apex of the polygon.
3. Ogive is useful in determining the partition values graphically.
4. While the pie chart is perhaps the most ubiquitous statistical chart in the business
world and the mass media, it is rarely used in scientific or technical publications

10. Histogram
The histogram is composed of a set of rectangles one over each class-interval
on the horizontal to the frequencies of the classes. Thus in case of equal class
interval the heights of the rectangles will be proportional to the frequencies
while for classes of unequal width, the heights of the rectangles will be
proportional to the ratios of the frequencies to the width of the corresponding
classes.

11. Example 01: Draw a histogram for the following data.

12. Frequency Polygon
• The frequency polygon of a grouped frequency distribution is constructed
by joining by means of straight lines the points whose abscissas are the mid-
points of the classes and the ordinates are the corresponding frequencies.
Thus a frequency polygon can also be obtained from a histogram by joining
the mid-points of the upper sides of the adjacent rectangles by means of
straight lines.
• To draw the frequency curve it is necessary first to draw the polygon. The
polygon is then smoothened out keeping in view the fact that the area of the
curve should be equal to that of the histogram.

14. Cumulative Frequency Curve (Ogives)
To construct cumulative frequency curve or ogive it is necessary first to form
the frequency table. Then the upper limits of the classes are taken as the x-
coordinates and the cumulative frequencies as the y-coordinates and the points
are plotted. The points are joined by a free hand smooth curve to give the
ogive.

15. Example 02: Draw a 'less than' ogive curve for the following data:

16. To Plot an Ogive:
• We plot the points with coordinates having abscissae as actual limits and
ordinates as the cumulative frequencies, (10, 2), (20, 10), (30, 22), (40, 40),
(50, 68), (60, 90), (70, 96) and (80, 100) are the coordinates of the points.
• Join the points plotted by a smooth curve.
• An Ogive is connected to a point on the X-axis representing the actual lower
limit of the first class.

17. Scale: X -axis 1 cm = 10 marks, Y -axis 1cm = 10 c.f.

18. Pie Chart
A pie chart (or a circle graph) is a circular chart divided into sectors, illustrating
relative magnitudes or frequences or percents. In a pie chart, the arc length of
each sector (and consequently its central angle and area), is proportional to the
quantity it represents. Together, the sectors create a full disk. It is named for its
resemblance to a pie which has been sliced

19. The following diagram shows the job occupied by the people in Trivandrum.
40%
38%
8%
14%
Job of people in Trivandrum
self business
govt employees
carpenters
private employees

20. CONCLUSION
• Frequency Distribution is a classification of data showing the number of
occurrences of each interval or category of a variable. In the case of a
quantitative variable the class intervals are arranged in order of magnitude.
• The graphical representation makes visual comparison of data easier and
gives a more lasting impression than is possible by any other means.
• There are 4 types of graph used to show frequency distribution. They are
Histogram, Frequency Polygon, Cumulative Frequency Curve and Pie Chart.

21. Thank you…,
#swih