Question

find the mode of the following data 0-5, 5-10, 10-15, 15-20, 20-25 frequency -2, 4,15,6,7​

Answer 1

We're provided with the following data:

$\begin{array}{|c|c|}\cline{1-2}\bf Class\ Interval & \bf Frquency\\\cline{1-2} \tt 0\ -\ 5 & 2\\\cline{1-2}\tt 5\ -\ 10 & 4\\\cline{1-2}\tt 10\ -\ 15 & 15\\\cline{1-2}\tt 15\ -\ 20 & 6\\\cline{1-2}\tt 20\ -\ 25 & 7\\\cline{1-2}\end{array}$

Formula to find the mode:

$\bf Z\ =\ l_1\ +\ \dfrac{f_1\ -\ f_0}{2f_1\ -\ f_0\ -\ f_2}\ \times\ i$

where,

• Z = mode
• l₁ = lower limit of the modal class
• f₁ = frequency of the modal class
• f₀ = frequency of the class preceding the modal class
• f₂ = frequency of the class succeeding the modal class
• i = height of the class intervals

From the data, it's clear that the modal class is 10 - 15, as it has the highest frequency.

From that data, we have:

• l₁ = 10
• f₁ = 15
• f₀ = 4
• f₂ = 6
• i = 5

Using these values in the formula,

$\tt Z\ =\ 10\ \times\ \dfrac{15\ -\ 4}{2(15)\ -\ 4\ -\ 6}\ \times\ 5\\\\\\Z\ =\ 10\ \times\ \dfrac{11}{20}\ \times\ 5\\\\\\Z\ =\ \dfrac{55}{2}\\\\\\\bf Z\ =\ 27.5$

Therefore, the mode is 27.5.