The weight of coffee (in gms) in 70 packets is given below :
| Weight (in gms) | 200 - 201 | 201 - 202 | 202 - 203 | 203 - 204 | 204 - 205 | 205 - 206 |
|---|---|---|---|---|---|---|
| No. of packets | 12 | 26 | 20 | 9 | 2 | 1 |
Determine the modal weight of coffee in a packet.
Solution:
Weight (in gms) No. of packets 200 - 201 12 $f_1$ 201 - 202 26 $f_m$ 202 - 203 20 $f_2$ 203 - 204 9 204 - 205 2 205 - 206 1 Here the maximum frequency $f_m = 26$.
The corresponding class 201 - 202 is the modal class.
$L = 201$, $f_m = 26$, $f_1 = 12$, $f_2 = 20$, $h = 1$$$ \text{Mode} = L + \left( \frac{f_m - f_1}{2f_m - f_1 - f_2} \right) h $$ $$ = 201 + \left( \frac{26 - 12}{2(26) - 12 - 20} \right) 1 $$ $$ = 201 + \left( \frac{14}{52 - 32} \right) $$ $$ = 201 + \left( \frac{14}{20} \right) $$ $$ = 201 + \left( \frac{7}{10} \right) $$ $$ = 201 + 0.7 $$ $$ = 201.7 $$Mode of weight of coffee is 201.7 gms.