Question

Calculate mode of the following sercies :
`{:("Class Interval",0-5,5-10,10-15,15-20,20-25,25-30,30-35),("Frequency"," "1," "2," "10," "4," "10," "9," "2):}`

Answer 1

Grouping of the frequencies is essential in this series, because there are two class intervals i.e., 10-15 and 20-25 with highest frequency , 10.
Hence , the grouping table and the subsequent Analysis Table are as following :

Analysis Table shown that f all the class intervals , 20-25 has the highest frequency (6). It has got the maximum (True) marks. Accordingly , 20-25 is the model class interval of the series. The actual value of mode is ,
`Z=l_(1)+(f_(1)-f_(0))/(2f_(1)-f_(0)-f_(2))xxi`
`l_(1)` = lower limit of model group =20
`f_(1)`= frequency of model class =10
`f_(0)` = frequency of class preceding the model class (15-20)=4
`f_(2)` frequency of class following the model class (25-30)=9
i = class interval =25-20=5
Hence, `Z=20+(10-4)/(20-4-9)xx5`
`=20+(6)/(7)xx5`
`=20+4.29`
24.29
Mode (Z) = 24.29