Question

Find the median and mode for the given data​

Answer 1

Answer:

Step-by-step explanation:

For Mode :

Since, the maximum cclass frequency is 12.

So, the model class is 12 - 16.

The lower boundary of the model class ( l ) = 12,

The class size ( h ) = 4,

The frequency of model class ( f1 ) = 12,

The frequency of the class preceding the model class ( f0 ) = 3,

The frequency of the class succeeding the model class ( f2 ) = 3.

Now by using the formula,

Mode = l + [ ( f1 - f0 ) / ( 2f1 - f0 - f2 ) ] × h

= 12 + [ ( 12 - 3 ) / ( 2 × 12 - 3 - 3 ) ] × 4

= 12 + [ 9 / 18 ] × 4

= 12 + (1/2)× 4

= 12 + 2

= 14 is the answer.

For Median :

C.l. = 0-4 4-8 8-12 12-16 16-20

f = 0 0 3 12 3

c.f. = 0 0 3 15 18

Number of observations ( n ) = 18,

So, n / 2 = 18 / 2= 9.

Therefore, 12 - 16 is the median class,

The lower boundary of the median clclass ( l ) = 12,

The c.f. of the class preceding the median class ( c.f. ) = 3,

The frequency of the median class ( f ) = 12,

The class size of the median class ( h ) = 4.

Now, by using the formula,

Median = l + [ (n / 2 - c.f.) / f ) × h

= 12 + [ ( 9 - 3 ) / 12 ] × 4

= 12 + [ 6 / 12 ] × 4

= 12 + ( 1/2 ) × 4

= 12 + 2

= 14 is the answer.