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Mathematics

Marks scored by students of class 10A and 10B in a particular class test are as follows:

MarksNo. of students of 10ANo. of students of 10B
1 - 512
6 - 1036
11 - 1583
16 - 20910
21 - 2547
26 - 3056
31 - 3564
36 - 4042

Draw their frequency polygons on the same graph.

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\dfrac{\text{(Lower limit of one class - Upper limit of previous class)}}{2}

= (6 - 5)2=12=0.5\dfrac{\text{(6 - 5)}}{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.

Continuous frequency distribution for given data is :

Classes before adjustmentClasses after adjustmentClass marksNo. of students of 10ANo. of students of 10B
1 - 50.5 - 5.5312
6 - 105.5 - 10.5836
11 - 1510.5 - 15.51383
16 - 2015.5 - 20.518910
21 - 2520.5 - 25.52347
26 - 3025.5 - 30.52856
31 - 3530.5 - 35.53364
36 - 4035.5 - 40.53842

Steps to draw frequency polygon :

  1. Take 1 cm along x-axis = 4 units.

  2. Take 1 cm along y-axis = 1 units.

  3. Find the mid-points of class-intervals.

  4. Find points corresponding to given frequencies of classes and the mid-points of class-intervals, and plot them.

  5. Join consecutive points by line segments.

  6. Join first end point with mid-point of class -5.5 - 0.5 with zero frequency and join the other end with mid-point of class 40.5 - 45.5 with zero frequency.

The required frequency polygon is shown alongside.

Marks scored by students of class 10A and 10B in a particular class test are as follows: Statistics, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

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