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Question

Calculate the median and third quartile using the following data:
Mid- Points marks515253545556575No. of students3101776421

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Solution

The cumulative frequency table for the data is given below.

MarksNo. of studentsCumulative FrequencyX(f)01033102010132030173030407374050643506044760702497080150

N2=25
Therefore, median class is 20-30.
Calculation of Median:
M=L1+N2c.ff×cM=20+251317×10M=27.05
Calculation of third quartile:
Class interval of Q3=(3N4)th term
=3(504) = 37.5th term
37.5th term corresponds to the class interval 40-50.
Q3=L1+3N4c.ff×CQ3=40+37.5376×10Q3=40.83


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