Calculate the median and third quartile using the following data:
Mid- Points marks515253545556575No. of students3101776421
The cumulative frequency table for the data is given below.
MarksNo. of studentsCumulative FrequencyX(f)0−103310−20101320−30173030−4073740−5064350−6044760−7024970−80150
N2=25
Therefore, median class is 20-30.
Calculation of Median:
M=L1+N2−c.ff×cM=20+25−1317×10M=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+3N4−c.ff×CQ3=40+37.5−376×10Q3=40.83