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Mathematics

If the class intervals 40 - 44, 45 - 49, 50 - 54 etc. in a frequency table are converted into continuous form, they become

  1. 40 - 45, 45 - 50, 50 - 55, etc

  2. 39 - 44, 44 - 49, 49 - 54, etc

  3. 39.5 - 44.5, 44.5 - 49.5, 49.5 - 54.5, etc

  4. any of the above

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Answer

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

Adjustment factor=Lower limit of one class - Upper limit of previous class2=45442=12=0.5\Rightarrow \text{Adjustment factor} = \dfrac{\text{Lower limit of one class - Upper limit of previous class}}{2} \\[1em] = \dfrac{45 - 44}{2} \\[1em] = \dfrac{1}{2} \\[1em] = 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.

The continuous frequency distribution is:

39.5 - 44.5, 44.5 - 49.5, 49.5 - 54.5, etc.

Hence option 3 is the correct option.

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