19.A survey was conducted by the Education
Ministry of India. The following distribution
gives the state-wise teachers-students ratio in
higha secondary schools of India.
Number of
states/U.T
Number of students per
teacher
15-20
20 - 25
25 - 30
30-33
Number of
states/U.T
3
8
Number of students per
teacher
35-40
40-45
45 - 50
50-55
10
i The modal dass is
2. 40-45
c. 50-55
6. 30-35
d. 25 - 30
ü. The mean of this data is
2. 19.2.
C
[ 39.2
b. 229
d. 292
The mode of the data is
2. 36.625
c. 32.625
b. 30.625
d. 31.625
iv. Half of (uppa-dass limit + lower class limit) is
a Class intaval
c. Class value
b. Classmark
d. Class size
The construction of the cumulative frequency table is useful in
determining the
a. Mean
b. Mode
Median
d. All of the above
Answers
Step-by-step explanation:
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.