2. ASPESS
• A pie chart is a circular statistical graphic, which
is divided into slices to illustrate numerical
proportion.
• In a pie chart, the arc length of each slice, is
proportional to the quantity it represents.
• The pie chart is an important type of data
representation. It contains different segments
and sectors in which each segment and sectors
of a pie chart forms a certain portion of the
total(percentage). The total of all the data is
equal to 360°. 2
3. ASPESS
Steps for calculation
• To work out with the percentage for a pie chart, follow
the steps given below:
1. Enter the data into the table.
2. Add all the values in the table to get the total.
3. Next, divide each value by the total and multiply by 100
to get a per cent
4. Calculate the degree
• Therefore, the pie chart formula is given as-
(Given Data/Total value of Data) × 360°
5. Draw a circle and use the protractor to measure the
degree of each sector.
3
4. ASPESS
How to Create a Pie Chart?
• Imagine a teacher surveys her class on the
basis of their favorite sports:
• Step -1
Enter the data into the table.
4
Name of
sports
Football Hockey Cricket Basketball Badminton
No. of
students
10 5 5 10 10
5. ASPESS
Step 2
Add all the values in the table to get the
total.
10+5+5+10+10
=40
N(TOTAL NO. OF FREQUENCY)
N=40
I.e. Total students are 40 in this case.
5
6. ASPESS
Step 3
• Next, divide each value by the total and
multiply by 100 to get a per cent:
• (Total no of student) N = 40
6
Football Hockey Cricket Basketball Badminton
(10/40) × 100
=25%
(5/ 40) × 100
=12.5%
(5/40) ×100
=12.5%
(10/ 40) ×100
=25%
(10/40)× 100
=25%
7. ASPESS
Step 4
To know how many degrees for each “pie
sector” we will take a full circle of 360° and
follow the calculations below:
The central angle of each component = (Value of each
component/sum of values of all the components)✕360°
7
Football Hockey Cricket Basketball Badminton
(10/ 40)× 360°
=90°
(5 / 40) × 360°
=45°
(5/40) × 360°
=45°
(10/ 40)× 360°
=90°
(10/ 40) ×
360°
=90°
8. ASPESS
Step 5
FOOTBALL, 29%
HOCKEY, 14%
CRICKET, 14%
BASKETBALL, 14%
BADMINTON, 29%
No. of student
FOOTBALL HOCKEY CRICKET BASKETBALL BADMINTON
8
9. ASPESS
• Ogives are graphs that are used to estimate how many numbers lie
below or above a particular variable or value in data.
• Ogive Graph or the cumulative frequency graphs are used to find
the median of the given set of data. If both, less than and greater
than, cumulative frequency curve is drawn on the same graph, we
can easily find the median value.
• To construct an Ogive, firstly, the cumulative frequency of the
variables is calculated using a frequency table.
• The Ogive is a graph of a cumulative distribution, which explains
data values on the horizontal plane axis and either the cumulative
relative frequencies
9
10. ASPESS
METHODS
• The two methods of Ogives are:
• Less than Ogive
• The frequencies of all preceding classes are added to the frequency
of a class. This series is called the less than cumulative series. It is
constructed by adding the first-class frequency to the second-class
frequency and then to the third class frequency and so on. The
downward cumulation results in the less than cumulative series.
• Greater than or More than Ogive
• The frequencies of the succeeding classes are added to the
frequency of a class. This series is called the more than or greater
than cumulative series. It is constructed by subtracting the first
class, second class frequency from the total, third class frequency
from that and so on. The upward cumulation result is greater than or
more than the cumulative series.
10
11. ASPESS
LESS THAN OGIVE
• STEP 1- Draw and mark the horizontal and
vertical axes.
• STEP 2 - Take the cumulative frequencies along
the y-axis (vertical axis) and the STEP 3 - upper-
class limits on the x-axis (horizontal axis).
• STEP 4 - Against each upper-class limit, plot the
cumulative frequencies.
• STEP 5 - Connect the points with a continuous
curve.
11
13. ASPESS
LESS THAN OGIVE
(4 , 4)
(10 , 8)
(20 , 12)
(28 , 16)
(32, 20)
0
5
10
15
20
25
30
35
4 8 12 16 20
CUMULATIVE
FREQUENCY
(Y)
MARKS (X)
MARKS
MARKS
13
14. ASPESS
MORE THAN OGIVE
• Draw and mark the horizontal and vertical
axes.
• Take the cumulative frequencies along the
y-axis (vertical axis) and the lower-class
limits on the x-axis (horizontal axis).
• Against each lower-class limit, plot the
cumulative frequencies.
• Connect the points with a continuous
curve.
14
15. ASPESS
MORE THAN OGIVE
MARKS FREQUENCY (f) C.F
0 - 4 4 32
4 – 8 6 28
8 – 12 10 22
12 – 16 8 12
16 – 20 4 4
15
LOWER CLASS
LIMIT
0 4 8 12 16
CUMULATIVE
FREQUENCY
32 28 22 12 4
POINTS (X , Y ) (0 , 32) (4 , 28) (8 , 22) (12 , 12) (16 , 4)
16. ASPESS
MORE THAN OGIVE
(0, 32)
(4 , 28)
(8 , 22)
(12 ,12)
(16 , 4)
0
5
10
15
20
25
30
35
0 4 8 12 16
CUMULATIVE
FREQUENCY
(Y)
MARKS (X)
Series 1
Series 1
16
17. ASPESS
Median By ogive Method
4
10
20
28
32
32
28
22
12
4
0
5
10
15
20
25
30
35
0 4 8 12 16
CUMULATIVE
FREQUENCY
(Y)
MARKS (X)
Chart Title
Series 1 Series 2
17
MEDIAN IS AT THE INTERSECTRING POINT OF BOTH THE OGIVE
