questions on statistics
the 1st and 3rd quartiles of a frequency distribution are 30 and 70. Also its coefficient of skewness is 0.6. The mean of the frequency distribution is____
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Given:Sk
b
=0.6,Q
3
+Q
1
=100,
Median=Q
2
=38
Sk
b
=
Q
3
−Q
1
Q
3
+Q
1
−2Q
2
⇒0.6=
Q
3
−Q
1
100−2×38
⇒Q
3
−Q
1
=
0.6
100−76
⇒Q
3
−Q
1
=
0.6
24
⇒Q
3
−Q
1
=
0.6
24
×
10
10
=
6
240
=40
⇒Q
3
−Q
1
=40 ..........(1)
⇒Q
3
+Q
1
=100 ..........(2)(given)
Adding (1) and (2), we get
2Q
3
=140
⇒Q
3
=
2
140
=70
Substituting the value of Q
3
in (2), we get
70+Q
1
=100
∴Q
1
=100−70=30
∴ upper quartile =70 and lower quartile =30
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