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The runs scored by two teams A and B on the first 42 balls in a cricket match are given below :

No. of ballsRuns scored by Team ARuns scored by Team B
1 - 625
7 - 1216
13 - 1882
19 - 24910
25 - 3045
31 - 3656
37 - 4263

Statistics

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Answer

The following frequency distribution is discontinuous, to convert it into continuous frequency distribution,

Adjustment factor = (Lower limit of one class - Upper limit of previous class) / 2

= 762=12\dfrac{7 - 6}{2} = \dfrac{1}{2}

= 0.5

Subtract the adjustment factor (0.5) from all the lower limits and add the adjustment factor (0.5) to all the upper limits.

Classes before adjustmentClasses after adjustmentClass markRuns by team ARuns by team B
1 - 60.5 - 6.53.525
7 - 126.5 - 12.59.516
13 - 1812.5 - 18.515.582
19 - 2418.5 - 24.521.5910
25 - 3024.5 - 30.527.545
31 - 3630.5 - 36.533.556
37 - 4236.5 - 42.539.563

Steps to draw frequency polygon :

Take 1 cm on x-axis = 6 balls and 1 cm on y-axis = 1 run.

For section A :

  1. Plot the points (3.5, 2), (9.5, 1), (15.5, 8), (21.5, 9), (27.5, 4), (33.5, 5) and (39.5, 6).

  2. Join the consecutive points by blue line segments.

  3. Join first end point with mid-point of class (-6.5) - 0.5 with zero frequency and join other end point with mid-point of 42.5 - 48.5.

The required frequency polygon is shown by blue line segments.

For section B :

  1. Plot the points (3.5, 5), (9.5, 6), (15.5, 2), (21.5, 10), (27.5, 5), (33.5, 6) and (39.5, 3).

  2. Join the consecutive points by black line segments.

  3. Join first end point with mid-point of class (-6.5) - 0.5 with zero frequency and join other end point with mid-point of 42.5 - 48.5.

The required frequency polygon is shown by black line segments.

The runs scored by two teams A and B on the first 42 balls in a cricket match are given below. Statistics, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

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