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Statistics Practice Test 1
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© examsnet.com
Question : 25
Total: 37
The heights of 50 students are tabulated asbelow:
Class interval (in cm)
Frequency
145 - 146
1
147 - 148
2
149 - 150
4
151 - 152
5
153 - 154
8
155 - 156
15
157 - 158
9
159 - 160
6
Which one of the following is correct about the distribution?
It is positively skewed
It is negatively skewed
It is symmetric
It is extremely asymmetric
None of these
Validate
Solution:
👈: Video Solution
C.I.
x
f
d
fd
cf
145 - 146
145.5
1
-8
-8
1
147 - 148
147.5
2
-6
-12
3
149 - 150
149.5
4
-4
-16
7
151 - 152
151.5
5
-2
-10
12
153 - 154
153.5
8
0
0
20
155 - 158
155.5
15
2
30
35
157 - 158
157.5
9
4
36
44
159 - 160
159.5
6
6
36
50
Σ f = 50
Σ fd = 56
A = Assumed; Mean = 153.5
Mean
=
A
+
Σ
f
d
Σ
f
=
153.5
+
56
50
= 153.3 + 1.12 = 154.62
Since,
n
2
=
50
2
=
25
∴ Median group is 155 - 156.
∴
l
=
115
,
h
=
2
,
c
=
20
,
f
=
15
Hence, Median
=
l
+
n
2
−
c
f
×
h
=
155
+
25
−
20
15
×
2
=
155.66
Since maximum frequency is 15, then the model group is 155 - 156.
∴
f
0
=
8
,
f
1
=
15
,
f
2
=
9
,
h
=
2
,
l
=
155
Mode
=
l
+
f
1
+
f
0
2
f
1
−
f
0
−
f
2
×
h
=
155
+
15
−
8
30
−
8
−
9
×
2
=
156.07
When rectangles are drawn and mean is the least and median lies between mode and mean, then distribution is negatively skewed.
© examsnet.com
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