GRAPHGRAPH

HISTOGRAMS

• It is a set of vertical bars with equal base but different heights.

• The histogram is also known as column diagram or bar graph or frequency histogram.

• Axis:x- axis - midpointsy- axis - frequency

Histogram Sample

0102030405060708090

100

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FREQUENCY POLYGON

• It essentially a line graph for the graphical representation of the frequency distribution.

• Many angled closed figure.• Axis:

x- axis - midpointsy- axis - frequency

Cumulative Frequency Curve

• Dd• Axis:

x- axis – exact upper limitsy- axis – cumulative frequency

CUMULATIVE PERCENTAGE CURVE / OGIVE CURVE

• In the case of Ogive, percentage of cumulative frequencies are plotted on the exact upper limits of each class interval

• Axis:x- axis – exact upper limity- axis – cumulative percentagecumulative percentage = (cum.f / N) x 100

PIE DIAGRAMS

• Pie or sector chart is a circle diagram. The name pie diagram has been derived from the word pie. The diagram looks like a pie and its parts look like slices cut from a pie. The pie diagram is drawn on the basis of percentage of data.

HISTOGRAM

ECI CI f

49.5 – 54.5 50 – 54 0

44.5 – 49.5 45 – 49 5

39.5 – 44.5 40 – 44 6

34.5 – 39.5 35 – 39 5

29.5 – 34.5 30 – 34 10

24.5 – 29.5 25 – 29 3

19.5 – 24.5 20 – 24 4

14.5 – 19.5 15 – 19 2

9.5 – 14.5 10 – 14 5

4.5 – 9.5 5 – 9 0

    N=40

Frequency Polygon

• A frequency polygon is a line graph representing a frequency distribution. It is an effective graph for comparing two (or) more frequency distributions. A frequency polygon is constructed from a histogram by joining the mid-points of the tops of various rectangles by straight lines.

FREQUENCY POLYGON

Mid-Point Class Interval Frequency

52 50 – 54 047 45 – 49 542 40 – 44 637 35 – 39 532 30 – 34 1027 25 – 29 322 20 – 24 417 15 – 19 212 10 – 14 57 5 – 9 0

N=40

SOLUTION:

Frequency Curve

• It is a free hand diagram. It cannot draw by scale. It is complete graph. It is an effective graph for comparing two (or) more frequency distributions.

Cumulative Frequency Curve

• The cumulative frequency corresponding to any class interval is the number of cases within that interval plus all the cases in intervals is the number of cases within that interval plus all the cases in intervals lower to it on the scale. Cumulative frequency curve is a free hand diagram.

Ogive or Cumulative Frequency Percentage Curve

• Ogive curve is a cumulative frequency Percentage curve. This can be classified into less than ogive curve and more than ogive curve. In less than ogive curve the upper limit of each class interval is taken on x-axis in increasing order. For each such upper limit on ‘x’ axis, the cumulative frequency of the entire class interval to that class interval is taken on ‘y’ axis.

Ogive Exact Limit Class Interval f cf

44.5 - 49.5 45 - 49 8 50

39.5 - 44.5 40 - 44 6 42

34.5 - 39.5 35 - 39 6 36

29.5 - 34.5 30 - 34 11 30

24.5 - 29.5 25 - 29 10 19

19.4 - 24.5 20 - 24 3 9

14.5 - 19.5 15 - 19 3 6

9.5 - 14.5 10 - 14 2 3

4.5 - 9.5 5 - 9 1 1

N = 50

GRAPH AXES

s.no Graph X-AXIS Y-AXIS

1 Histogram EXACT CLASS LIMIT FREQUENCY

2 Frequency Polygon MID POINT FREQUENCY

3 Frequency Curve MID POINT FREQUENCY

4 Cumulative Frequency Curve EXACT UPPER LIMIT CF

5 Ogive Curve EXACT UPPER LIMIT CF

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