Question

The marks in science of 80 students of class X are given below: Find the mode of the marks obtained by the students in science.
Marks: 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100
Frequency: 3 5 16 12 13 20 5 4 1 1

Answer 1

Answer:

mode =52.5

Given:-

• the marks in scienceof 80 student of class X are given below

$marks \: \: \: \: \: \: \: \: \: \: \: \: frequency \\ \\ 0 - 10 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 3 \\ 10 - 20 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 5 \\ 20 - 30 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 16 \\ 30 - 40 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 12 \\ 40 - 50 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 13 \\ 50 - 60 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 20 \\ 60 - 70 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 5 \\ 70 - 80 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 4 \\ 80 - 90 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 1 \\ 90 - 100 \: \: \: \: \: \: \: \: \: \: \: \: \: \: 1$

To find :-

• Mode of the marks obtain by the student in science....

Solution:-

$here \\ \\ the \: higher \: frequency = 20 \\ \\ there \: for \\ \: modal \: class \: = 50 - 60 \\ \\ f_{0} = 13 \\ f_{1} = 20 \\ f_{2} = 5 \\ h = 10 \\ l = 50 \\ \\ mode =l + \frac{f_{1} - \: f_{0} }{2f_{1 -f_{0} - f_{2} }} \times h \\ \\ mode = 50 + \frac{20 - 13}{2 \times 20 - 13 - 5} \times 10 \\ \\ mode = 50 + \frac{7}{40 - 18} \times 10 \\ \\ mode = 50 + \frac{7}{28} \times 10 \\ \\ mode = 50 + 2.5 \\ \\ mode = 52.5$