Question

estimate the median and mode, is the this distribution symmetrical or skewed?

Frequency Distribution:

1.5 to 4.5    3

4.5 to 7.5    5

7.5 to 10.5    9

10.5 to 13.5    5

13.5 to 16.5    3

Answer 1

To find Median Class
= value of (n/2)th observation

= value of (25/2)th observation

= value of 12th observation

From the column of cumulative frequency cf, we find that the 12th observation lies in the class

7.5-10.5.

∴ The median class is 7.5-10.5.

Now,
∴L=lower boundary point of median class =7.5

∴n=Total frequency =25

∴cf=Cumulative frequency of the class preceding the median class =8

∴f=Frequency of the median class =9

∴c=class length of median class =3

Median M= L+((n/2-cf)/f) * c

=7.5+((12-8)/9)*3

=9.

To find Mode Class
Here, the maximum frequency is 9.

∴ The mode class is 7.5-10.5.

∴L=lower boundary point of mode class =7.5

∴f1= frequency of the mode class =9

∴f0= frequency of the preceding class =5

∴f2= frequency of the succeeding class =5

∴c= class length of mode class =3

Z=L+((f1-f0)/(2*f1-f0-f2))*c

=7.5+((9-5)/(2*9-5-5))*3

=9

Mean =∑f*x/∑f

=225/25

=9

Here, Median = Mode = Mean

Therefore, We conclude that distribution is symmetric.

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