Question

please answer....first answer will be mark as a brainlist​

Answer 1

Answer:

Question:

Find the median of the following distribution:

$\boxed{\begin{array}{c|c} \sf{Classes}&\sf{Frequency} \\ \sf{} & \sf{} & \sf{} \\ 0-10&8\\10-20&12 \\ 20-30 & 10 \\ 30-40 & 11 \\ 40-50 &9 \end{array}}$

Formula required:

Formula to calculate the median of grouped data

   $\boxed{\sf{Median = l + \Bigg(\dfrac{\dfrac{N}{2}-F}{f}\Bigg)\times h}}\;\;\bigstar$

Where,

l = lower limit of median class

f = frequency of the median class

h = size of the median class

F = cumulative frequency of the class preceding the median class

Solution:

Let's first draw cumulative frequency table

$\boxed{\begin{array}{c|c|c} \sf{Classes}&\sf{Frequency}&\sf{Cumulative\;frequency} \\ \sf{} & \sf{} & \sf{} \\ 0-10&8&8\\10-20&12&20 \\ 20-30 & 10&30 \\ 30-40 & 11 &41\\ 40-50 &9&50 \\ \sf{} & \overline{\;\;\;\;\sf{N=50}\;\;\;\;} & \sf{} \end{array}}$

Now, we have N = 50

so, N/2 = 50/2 = 25

The cumulative frequency just greater than N/2 is class 20-30 hence, it is our median class.

so,

we will have,

l = 20

N = 50

F = 20

f = 10

h = 10

Using Formula to calculate Median

$\implies\sf{Median = l + \Bigg(\dfrac{\dfrac{N}{2}-F}{f}\Bigg)\times h}$

$\implies\sf{Median = 20 + \Bigg(\dfrac{\dfrac{50}{2}-20}{10}\Bigg)\times 10}$

$\implies\sf{Median = 20 + \Bigg(\dfrac{25-20}{10}\Bigg)\times 10}$

$\implies\boxed{\boxed{\sf{Median = 25}}}\;\;\;\bigstar$

Therefore,

MEDIAN of the given frequency distribution is 25.

Answer 2

S O L U T I O N :

$\underline{\bf{Given\::}}$

Classes =       1 - 10 , 10 - 20 , 20 - 30 , 30 - 40 , 40 - 50

Frequency =     8           12           10            11            9

$\underline{\bf{Explanation\::}}$

Data shown :

$\begin{tabular}{|c|c|c|} \cline{1-3}\multicolumn{3} {|c|} {DATA} \\ \cline{1-3} \bf Classes & \bf Frequency, (f) & \bf Cumulative - frequency \\ \cline{1-3} 0-10 & 8 & 8 \\ 10-20 & 12 & 20 \\ 20-30 & 10 & \bf M = 30 \\ 30-40 & 11 & 41 \\ 40-50 & 9 & 50 \\ \cline{1-3} & \sf N = \sf \Sigma \sf f = \sf 50 & \\ \cline{1-3} \end{tabular}}$

A/q

As we know that formula of the median;

$\boxed{\bf{Median, (M) = l + \bigg(\frac{n/2 - CF}{f} \bigg) \times h}}$

We have :

• l = 20
• CF = 20
• f = 10
• h = 10

Now,

$\mapsto\tt{Median = l + \bigg(\dfrac{n/2 - CF}{f} \bigg) \times h}$

$\mapsto\tt{Median = 20 + \bigg(\dfrac{50/2 - 20}{10} \bigg) \times 10}$

$\mapsto\tt{Median = 20 + \bigg(\dfrac{\cancel{50/2} - 20}{10} \bigg) \times 10}$

$\mapsto\tt{Median = 20 + \bigg(\dfrac{25 - 20}{10} \bigg) \times 10}$

$\mapsto\tt{Median = 20 + \dfrac{5}{10} \times 10}$

$\mapsto\tt{Median = 20 + \dfrac{5}{\cancel{10}} \times \cancel{10}}$

$\mapsto\tt{Median = 20 + 5 \times 1}$

$\mapsto\tt{Median = 20 + 5 }$

$\mapsto\bf{Median = 25}$

Thus,

The median of these data will be 25 .