Question

find the mode of the following data given ( statistics chapter)​

Answer 1

Answer:

Required Table :-

$\begin{gathered} \begin{gathered} \boxed{ \boxed{ \begin{array}{lclcl} \bf \: {ci} \:& \bf{f} \\ \\ \rm 15 - 20 \: & \: 3 \\ \\ \rm20 - 25&8 \\ \\ \rm \: 25 - 30 \: & \: 9 ( f_{0})\\ \\ \rm(l)30 - 35 \: & \: 10 ( f_{1}) \\ \\ \rm \: 35 - 40&3( f_{2}) \\ \\ \rm40 - 45&0 \\ \\ \rm45 - 50&0 \\ \\ \rm50 - 55&2 \end{array}}}\end{gathered} \end{gathered}$

From Table,

• lower boundary (l) = 30

• f1 = 10, f0 = 9 , f2 = 3

• height (h) = 30 - 25 = 5

We know that,

• ${ \sf{Mode = l + \bigg( \frac{ f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2} } \bigg) \times h}}$

Let's substitute those values in formula,

${ \implies{ \sf{Mode = 30 + \bigg( \frac{10 - 9}{2(10) - 9 - 3} \bigg) \times 5}}} \\ \\ \implies{ \sf{Mode = 30 + \bigg( \frac{1}{20 - 12} \bigg) \times 5}} \\ \\\implies{ \sf{Mode = 30 + \bigg( \frac{1}{8} \bigg) \times 5 }} \\ \\ \implies{ \sf{Mode = 30 + \frac{5}{8} }} \\ \\ \implies{ \sf{Mode = 30 + 0.625}} \\ \\ \implies{ \sf{Mode = 30.62}}$

Therefore,

• Mode of given data = 30.62