Compute the median of the following data:
Marks 80-90 90-100 100-110 110-120 120-130 130-140 140- 150
150- 160
Frequency 9 17 19 45 33 15 12 0
Answers
Answer:
AccordingtotheQuestion
\begin{gathered}\begin{array}{|c|c|c|}\cline{1-3}Marks\;Obtained & Number\;of\;Students(f) & C.F \\ \\ \cline{1-3} 140-150 & 12 & 12 \\ \\ \cline{1-3} 130-140 & 27-12=15 & 27 \\ \\ \cline{1-3} 120-130 & 60-27=33 & 60 \\ \\ \cline{1-3} 110-120 & 105-60=45 & 105 \\ \\ \cline{1-3} 100-110 & 124-105=19 & 124 \\ \\ \cline{1-3} 90-100 & 141-124=17 & 141 \\ \\ \cline{1-3} 80-90 & 150-141=9 & 150 \end{array}\end{gathered}
\cline1−3MarksObtained
\cline1−3140−150
\cline1−3130−140
\cline1−3120−130
\cline1−3110−120
\cline1−3100−110
\cline1−390−100
\cline1−380−90
NumberofStudents(f)
12
27−12=15
60−27=33
105−60=45
124−105=19
141−124=17
150−141=9
C.F
12
27
60
105
124
141
150
N = 150
\tt{arrow\dfrac{n}{2}=75}arrow
2
n
=75
\because\boxed{Median\;class\;is\;110-120}∵
Medianclassis110−120
Here we have :-
\tt{arrow\dfrac{n}{2}=75}arrow
2
n
=75
l = 110, f = 45 , C.F = 60 and h = 10
\tt{arrow Median=\dfrac{n/2-C.F}{f}\times h}arrowMedian=
f
n/2−C.F
×h
\tt{arrow 110 + \dfrac{75-60}{45}\times 10}arrow110+
45
75−60
×10
\tt{arrow 110 + \dfrac{150}{45}\times 10}arrow110+
45
150
×10
= 110 + 3.33
= 113.33
{\boxed{Here\;Median\;=113.33\; marks}}
HereMedian=113.33marks
Step-by-step explanation:
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