Question

c.I.1-5,5-9,9-13,13-17,17-21....f.7,2,2,8,1.find mean ,median,mode.​

Answer 1

Mean = 9.8

Median = 11

Mode = 14.8462

Step-by-step explanation:

Class Interval       frequency(f)      Mid value (x)        f(x)          cf

1-5                             7                          3                     21            7

5-9                             2                         7                     14            9

9-13                           2                         11                     22          11

13-17                          8                         15                   120         19

17-21                          1                         19                    19           20

                             n = 20                                      ∑f(x) = 196

Mean $\bar{x}=\frac{\sum fx}{n}$

             $=\frac{196}{20}$

Mean = 9.8

To find median class

= value of $(\frac{n}{2})th$ observation

= value of $(\frac{20}{2})th$ observation

= value of 10th observation

From the column of cumulative frequency cf, we find that the 10th observation lies in the class 9-13.

∴ The median class is 9-13.

Now,

$Median M=L+\frac{\frac{n}{2}-cf }{f}\times c$

L=lower boundary point of median class =9

n=Total frequency =20

cf=Cumulative frequency of the class preceding the median class =9

f=Frequency of the median class =2

c=class length of median class =4

$=9+\frac{1}{2}\times 4$

= 9 + 2

= 11

Median = 11

To find Mode Class

Here, maximum frequency is 8.

∴  The mode class is 13-17.

$Z=L+(\frac{f_1-f_0}{2\times f_1-f_0-f_2} )\times c$

L=lower boundary point of mode class =13

f1= frequency of the mode class =8

f0= frequency of the preceding class =2

f2= frequency of the succeeding class =1

c= class length of mode class =4

  $=13+(\frac{8-2}{2\times 8-2-1} )\times 4$

  =  $13+(\frac{6}{13} )\times 4$

  = 13 + 1.8462

Mode = 14.8462

Learn more about median : https://brainly.in/question/15606278

Answer 2

Step-by-step explanation:

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