Frequency Diagrams

ByMr. Swatanter SinghPGT (ECO.) KV HISAR CANTT.

Previous knowledge testing

• What do you mean by presentation of data ?

• What is frequency ?• What is bar diagram ?• What is cumulative frequency ?• What is continuous variable ?

Types of frequency diagrams

• Histogram• Frequency polygon • Frequency curve• Ogive

Histogram

Histogram is a graphical presentation of frequency distribution. It is in the form of adjacent rectangles. It is a two dimensional diagram. It means height and width of rectangular bars both are important for the comparison of data.

HistogramMarks No. of

students

10-20 3

20-30 13

30-40 30

40-50 22

50-60 12

60-70 2

Frequency Polygon

Two methods• Ist method : Frequency Polygon is drawn by

joining the mid points of the top sides of the consecutive rectangles.

• IInd method :The frequency polygon may be drawn by connecting points plotted against the frequencies at the midpoints of the classes.

Frequency PolygonIst method

Marks No. of students

10-20 3

20-30 13

30-40 30

40-50 22

50-60 12

60-70 2

Frequency PolygonIInd method

Marks No. of students

10-20 3

20-30 13

30-40 30

40-50 22

50-60 12

60-70 2

Frequency Curve

Frequency curve is a smooth free hand curve passing through the points of frequency polygon as closely as possible.

Frequency Curve

Ogive

Ogive is a cumulative frequency curve. Two Types : Less than Ogive : is obtained by joining the

points for cumulative frequencies plotted against the upper class limit of class intervals.

More than Ogive : is obtained by joining the points for cumulative frequencies plotted against the lower class limit of class intervals.

Less than Ogive

Marks

No. of students

Less than Ogive

10-20

3 3

20-30

13 16

30-40

30 46

40-50

22 68

50-60

12 80

60-70

2 82

More than Ogive

Marks

No. of students

Less than Ogive

10-20

3 3

20-30

13 16

30-40

30 46

40-50

22 68

50-60

12 80

60-70

2 82

Determination of median

Median is the value corresponding to the intersection point of less than and more than ogives.

Uses 0f Frequency Diagrams

• to display large amounts of data in a relatively simple chart form.

• to tell frequency of occurrence.• to easily see the distribution of the data.• to see if there is variation in the data.• to make future predictions based on the

data.

• Define histogram.Define histogram.• Define frequency polygon.Define frequency polygon.• Plot histogram and frequency polygon for the given set of data:Plot histogram and frequency polygon for the given set of data:

• Define ogive.Define ogive.• How Median is graphically determined ?How Median is graphically determined ?

Income 1000-2000 2000-3000 3000-4000 4000-5000 5000-6000

No of employees

20 25 10 50 15

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