Question

The table shows the daily expenditure on grocery of 25 households in a locality. Find the modal daily expenditure on grocery by a suitable method. Daily Expenditure (in Rs.) 100-150 150-200 200-250 250-300 300-350 No of households 4 5 12 2 2

Answer 1

"Concept:  The mode value of grouped data.

Daily Expenditure

( in Rupees)        100-150        150-200  $(f_0)$       200-250 $(f_1)$      250-300 $(f_2)$        300-350

Number of Households        4        5        12        2        2

We know that, $mode\quad =l+\frac { { f }_{ \left( 1-{ f }_{ 0 } \right)  } }{ { 2f }_{ \left( 1-{ f }_{ 0 }-{ f }_{ 2 } \right) } } \times h$

Modal class = The range of values with the highest frequency

In this problem, the modal class is 200 - 250

$f_0$ = The frequency of the modal class = 12

$f_1$ = The frequency of the class that is present before the modal class = 5

$f_2$= The frequency of the class that is  present after the modal class = 2

h = Class interval = (250 -200) = 50.

l = lower limit of the modal class = 200.

Substituting the above values,

$Mode =200+\frac { (12-5) }{ (2(12)-5-2) }\times50$

$=200+\frac { 7 }{ (24-5-2) } \times 50$

$=200+\frac { 7 }{ 17 } \times 50$                          

$= 200 + (0.412) \times 50$

= 200 + 20.59

Mode = 220.59"