Question

Cand e mode of the following series
Ci 0-5. 20
5-10. 24
10-15 32
15-20 28
20-25 20
25-30. 26​

Answer 1

We're provided with the following data:

$\begin{array}{|c|c|}\cline{1-2}\bf Class\ Interval & \bf Frequency\\\cline{1-2}\tt 0\ -\ 5 & 20\\\cline{1-2}\tt 5\ -\ 10 & 24\\\cline{1-2}\tt 10\ -\ 15 & 32\\\cline{1-2}\tt 15\ -\ 20 & 28\\\cline{1-2}\tt 20\ -\ 25 & 20\\\cline{1-2}\tt 25\ -\ 30 & 26\\\cline{1-2}\end{array}$

Formula to find the mode:

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

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 = 32
• f₀ = 24
• f₂ = 28
• i = 5

Using these values in the formula,

$\tt Z\ =\ 10\ \times\ \dfrac{32\ -\ 24}{2(32)\ -\ 24\ -\ 28}\ \times\ 5\\\\\\Z\ =\ 10\ \times\ \dfrac{8}{12}\ \times\ 5\\\\\\\bf Z\ =\ 33.33\ [approx.]$

Therefore, the mode is 33.33.

Answer 2

$\large \green{ \fcolorbox{grey}{white}{ ☑ \: \textbf{Verified \: answer}}}$

$\begin{gathered} \boxed{\begin{array}{|c|c|}\bf Class\ Interval & \bf Frequency\\\tt 0\ -\ 5 & 20\\\tt 5\ -\ 10 & 24\\ \tt 10\ -\ 15 & 32\\\tt 15\ -\ 20 & 28\\\tt 20\ -\ 25 & 20\\\tt 25\ -\ 30 & 26\\\end{array}}\end{gathered}$