Cumulative-Frequency Curve

Group data are also represented by a curve called ogive or cumulative-frequency curve. As the name suggests, in this representation cumulative frequencies of different class intervals play an important role.


Method of Constructing on Ogive:

Step I: Prepare a frequency-distribution table with overlapping class intervals to make the distribution continuous.

Step II: Prepare the cumulative-frequency table for the distribution.

Step III: Plot points on the horizontal axis (class-interval axis) corresponding to the upper limits of the class intervals.

Step IV: Draw perpendicular to the horizontal axis at the points representing upper limits of the class intervals. The length of the perpendiculars should represent the cumulative frequencies of the corresponding class intervals. In other words, plot points with coordinates (a, c), where a = upper limit of a class interval and c = the corresponding cumulative frequency.

Step V: Join the points plotted in step IV freehand to get a smooth curve.

Step VI: Join the first point to the point representing the lower limit of the first class interval in continuation with the smooth curve in step V. (This part of the curve may be a dotted line segment.)


Example: Draw an ogive for the following distribution.

Class Interval

0 - 20

20 - 40

40 - 60

60 - 80

80 - 1000

Frequency

4

6

5

3

2

Solution:

The cumulative-frequency table for the distribution is as given below.

Class Interval

0 - 20

20 - 40

40 - 60

60 - 80

80 - 1000

Frequency

4

6

5

3

2

Cumulative Frequency

4

10

(4 + 6)

15

(4 + 6 + 5)

18

(4 + 6 + 5 + 3)

20

(4 + 6 + 5 + 3 + 2)

Now, plot the points (20, 4), (40, 10), (60, 15), (80, 18) and (100, 20) following the steps 3 and 4, and join the points following step 5 and 6. We get the following ogive.

Cumulative-Frequency Curve

Scale: On the x-axis, 1 cm = width of interval.

          On the y-axis, 2 mm = cumulative-frequency 1.


Note: The ogive discussed above is also known as “less than” ogive.

A “more than” ogive can also be drawn by considering “more than” cumulative frequencies for the class intervals. The cumulative-frequency table for “more than” ogive in the above example will be as below.

Class Interval

0 - 20

20 - 40

40 - 60

60 - 80

80 - 1000

Frequency

20

16

(20 - 4)

10

(16 - 6)

5

(10 - 5)

2

(5 - 3)

Now, plotting the points (0, 20), (20, 16), (40, 10), (60, 5), (80, 2) [i.e., (lower limit, “more than” cumulative frequency)] and joining them by a smooth curve, we get the “more than” ogive.


Utility of Ogives:

An ogive for a frequency distribution displays cumulative frequencies of different class intervals. As such it helps to find the median, and the upper and lower quartiles of a distribution which will be discussed later in this book.




10th Grade Math

From Cumulative-Frequency Curve to HOME PAGE



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Expanded form of Decimal Fractions |How to Write a Decimal in Expanded

    Jul 22, 24 03:27 PM

    Expanded form of Decimal
    Decimal numbers can be expressed in expanded form using the place-value chart. In expanded form of decimal fractions we will learn how to read and write the decimal numbers. Note: When a decimal is mi…

    Read More

  2. Worksheet on Decimal Numbers | Decimals Number Concepts | Answers

    Jul 22, 24 02:41 PM

    Worksheet on Decimal Numbers
    Practice different types of math questions given in the worksheet on decimal numbers, these math problems will help the students to review decimals number concepts.

    Read More

  3. Decimal Place Value Chart |Tenths Place |Hundredths Place |Thousandths

    Jul 21, 24 02:14 PM

    Decimal place value chart
    Decimal place value chart are discussed here: The first place after the decimal is got by dividing the number by 10; it is called the tenths place.

    Read More

  4. Thousandths Place in Decimals | Decimal Place Value | Decimal Numbers

    Jul 20, 24 03:45 PM

    Thousandths Place in Decimals
    When we write a decimal number with three places, we are representing the thousandths place. Each part in the given figure represents one-thousandth of the whole. It is written as 1/1000. In the decim…

    Read More

  5. Hundredths Place in Decimals | Decimal Place Value | Decimal Number

    Jul 20, 24 02:30 PM

    Hundredths Place in Decimals
    When we write a decimal number with two places, we are representing the hundredths place. Let us take plane sheet which represents one whole. Now, we divide the sheet into 100 equal parts. Each part r…

    Read More