Question

any body plz answer my question plz​

Answer 1

Question

Calculate the mode of the following distribution.

$\begin{tabular}{|c|c|}\cline{1-2}Marks(CI) & No\;of\:students(f)\\ \cline{1-2}0-10 & 20\\ 10-20 & 24 \\ 20-30 & 40 \\30-40 & 36 \\40 -50 & 20 \\\cline{1-2}\end{tabular}$

Solution

▶ Formula for calculating mode

$\boxed{\sf{Mode=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)h}}$

( where l is the lower limit of modal class , f₁ is the frequency of modal class,  f₀ is the frequency of class preceding the modal class , f₂ is the frequency of class succeeding  the modal class and h is the class height )

In the given Question

$\bullet\:\;\sf{l=20}\\\bullet\:\;\sf{f_1=40}\\\bullet\:\;\sf{f_0=24}\\\bullet\:\;\sf{f_2=36}\\\bullet\:\;\sf{h=10}$

so,

$\implies\;\sf{mode=20+\left(\frac{40-24}{2(40)-24-36}\right)\times 10}\\\\\implies\;\sf{mode=20+\left(\frac{16}{20}\right)\times 10}\\\\\implies\;\boxed{\boxed{\sf{mode=28}}}$

Hence, the mode of the data is 28 .