14. The table below gives the frequency distribution of the number of teachers in Higher Secondary School in 2012 in India. Find the average number of teachers per Higher Secondary School in India for 2012. Number of Teachers Number of H.S. Schools 6-10 955 10-15 1067 16-20 1663 21-25 1492 26-30 1220 31-35 1129 36-40 745 41-45 637 46-50 442
Answers
Answer:
No. of students per teacher x
i
No. of states/U.T.
(f
i
) f
i
x
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
Σf
i
x
i
=
35
1022.5
=29.21
As frequency is maximum for the class 30-35, modal class is 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 class preceding the modal class = 9
f
2
= frequency of class succeding the modal class = 3
h= higher limit - lower limit = 35 - 30 = 5
Mode=30+
2×10−(9+3)
10−9
×5
⇒mode=30+
8
1
×5=30+0.625=30.625
Hence, the mean and modal given data are 29.21 and 30.625 respectively.
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