number of students per teacher
15-20 3
20-25 8
25-30 9
30-35 10
35-40 3
40-45 0
45-50 0
50-55 2
find mode and mean of data
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10th
Maths
Statistics
Mode of Grouped Data
The following distribution ...
STATISTICS
The following distribution gives the state-wise teacher student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.
No. of students per teacher
No. of state/ U.T.
15-20
3
20-25
8
25-30
9
30-35
10
35-40
3
40-45
0
45-50
0
50-55
2
MEDIUM
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ANSWER
Answer:- x
i
=
2
lower limit + upper limit
No. of students
per teacher x
i
No. of state
(f
i
) x
i
×f
i
=x
i
f
i
15-20 17.5 3 52.5
20-25 22.5 8 180
25-30 27.5 9 247.5
30-35 32.5 10 325
35-40 37.5 3 112.5
40-45 42.5 0 0
45-50 47.5 0 0
50-55 52.5 2 105
Σf
i
=35 Σf
i
x
i
=1022.5
∴Mean=
Σf
i
Σx
i
f
i
=
35
1022.5
=29.2
Here, maximum frequency '10' is of classs interval '30-35'.
$$ \therefore Modal class = 30 - 35.
∴Mode=L+
2f
1
−f
0
−f
2
f
1
−f
0
×h
where
L = Lower limit of modal class =30
f
1
= frequency of modal class =10
f
0
= frequency of previoous class =9
f
2
= frequency of next class =3
h = width of class =35−30=5
∴Mode=30+
2(10)−9−3
10−9
×5=30+
8
1
×5=30.625
∴ D) Mode =30.625 & Mean =29.2.
hope it helps...!!