Question

From the following compute Median and Mode
No of employees Income
5 0-10
7 10-20
15 20-30
25 30-40
20 40-50
15 50-60
8 60-70
5 70-80

Answer 1

X	f	c.f
0-10	5	5
10-20	7	12
20-30	15	27
30-40	25	52
40-50	20	72
50-60	15	87
60-70	8	95
70-80	5	100

$$\begin{gathered} \mathbf{Calculation}\mathbf{}\mathbf{of}\mathbf{}\mathbf{Median} \\ \mathrm{Size}\mathrm{of}{\left(\frac{N}{2}\right)}^{\mathrm{th}}\mathrm{item}=\frac{100}{2}=50 \\ \mathrm{This}\mathrm{corresponds}\mathrm{to}\mathrm{the}\mathrm{class}\mathrm{interval}(30-40) \\ \mathrm{Median}=\mathit{}l+\frac{({\displaystyle \frac{N}{\mathit{2}}}\mathit{}\mathit{-}\mathit{}c\mathit{.}f\mathit{.})}{f}\times i \\ \mathrm{Subsituting}\mathrm{the}\mathrm{values} \\ \mathrm{Median}=\mathit{}30+\frac{(50\mathit{}\mathit{-}\mathit{}27)}{25}\times 10 \\ \mathrm{Median}=39.2 \\ \mathbf{Calculation}\mathbf{}\mathbf{of}\mathbf{}\mathbf{Mode} \\ \mathrm{The}\mathrm{class}\mathrm{interval}\mathrm{with}\mathrm{the}\mathrm{highest}\mathrm{frequency}\mathrm{is}(30-40).\mathrm{So},\mathrm{this}\mathrm{is}\mathrm{the}\mathrm{modal}\mathrm{class}. \\ \mathrm{Mode}=\mathit{}l+\frac{(f_1\mathit{}\mathit{-}\mathit{}{f}_{\mathit{0}})}{2f_1-f_0-f_2}\times \mathrm{i} \\ \mathrm{Mode}=30+\frac{(25\mathit{-}\mathit{}15)}{2\times 25-15-20}\times 10 \\ \mathrm{Mode}=36.66 \end{gathered}$$