Question

Grouped frequency distribution of supply of milk to hotels and the number of hotels is given in the following table. Find the mode of the supply of milk.
Milk (Litre) : No. of hotels
1-3 : 7
3-5 : 5
5-7 :15
7-9 : 20
9-11: 35
11-13 : 18

Answer 1

Answer:

Mode = 9.94 litres

Step-by-step explanation:

$\begin{tabular}{|l|l|l|}</p><p>\cline{1-3}</p><p>Class interval & Frequency(fi) & Remark \\ \cline{1-3}</p><p>1-3 & 7 & \\ \cline{1-3}</p><p>3-5 & 5 & \\ \cline{1-3}</p><p>5-7 & 15 & \\ \cline{1-3}</p><p>7-9 & 20 & f_0 \\ \cline{1-3}</p><p>9-11 & 35 & Modal class:f_1 \\ \cline{1-3}</p><p>11-13 & 18 & f_2 \\ \cline{1-3}</p><p>Total & & \\ \cline{1-3}</p><p>\end{tabular}$

$\boxed{Mode = l + \bigg(\frac{f1 - f0}{2f1 - f0 - f2} \bigg)h }$

l: lower class limit =9

h: class size= 2

f1:35

f0:20

f2:18

put these values in the formula

$Mode = 9+ \bigg(\frac{35 - 20}{2 \times 35 - 20 -18 } \bigg)2 \\ \\ = 9 + \bigg(\frac{15}{70 - 38}\bigg)2 \\ \\ = 9 + \frac{15}{32} \times 2 \\ \\ = 9 + \frac{15}{16} \\ \\ = 9 + 0.94 \\ \\ mode= 9.94$

Hope it helps you.