Question

Calculate the mode for the following frequency distribution:

Class interval	0-4	4-8	8-12	12-16
Frequency	4	8	5	6

Answer 1

As the class 4 - 8 has maximum frequency, it is the modal class.
Therefore,
x_k = 4, h = 4, f_k = 8, f_k-1 = 4, f_k+1 = 5
$\mathrm{Mode},{\mathrm{M}}_0={\mathrm{x}}_{\mathrm{k}}+\left\{\mathrm{h}\times \frac{\left({\mathrm{f}}_{\mathrm{k}}-{\mathrm{f}}_{\mathrm{k}-1}\right)}{\left(2{\mathrm{f}}_{\mathrm{k}}-{\mathrm{f}}_{\mathrm{k}-1}-{\mathrm{f}}_{\mathrm{k}+1}\right)}\right\}$
$=4+\left\{4\times \frac{\left(8-4\right)}{\left(2\times 8-4-5\right)}\right\}$
$$\begin{gathered} =4+\left\{4\times \frac{4}{16-9}\right\} \\ =4+\left\{4\times \frac{4}{7}\right\} \\ =\left(4+\frac{16}{7}\right) \\ =\left(\frac{28+16}{4}\right) \\ =\left(\frac{44}{7}\right) \\ =6.29 \end{gathered}$$