Question

Calculate median from data marks(less than) 10,20,30,40,50 and no.of students 3,8,17,20,22

Answer 1

Answer:

10,20,30,40,50 use formula m=n+1/2 , now m=5+1/2 = 3rd position number that is= 30 in this way u can find out the ans. of 2nd question please brain list the ans.

Answer 2

$\large\underline{\sf{Solution-}}$

The given series can be represented in exclusive series as

$\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c|c}\sf Class\: interval&\sf Frequency\: (f)&\sf \: cumulative \: frequency\\\frac{\qquad \qquad}{}&\frac{\qquad \qquad}{}\\\sf 0 - 10&\sf 3&\sf3\\\\\sf 10 - 20 &\sf 5&\sf8\\\\\sf 20-30 &\sf 9&\sf17\\\\\sf 30 - 40&\sf 3&\sf20\\\\\sf 40-50&\sf 2&\sf22\\\\\sf &\sf &\sf\\\frac{\qquad}{}&\frac{\qquad}{}\\\sf & \sf & \end{array}}\end{gathered}\end{gathered}\end{gathered}$

We know,

Median is given by

$\boxed{ \rm Median= l + \Bigg \{h \times \dfrac{ \bigg( \dfrac{N}{2} - cf \bigg)}{f} \Bigg \}}$

where,

• l denotes lower limit of median class

• h denotes width of median class

• f denotes frequency of median class

• cf denotes cumulative frequency of the class preceding the median class

• N denotes sum of frequency

According to the question,

N/ 2 = 22/2 = 11

Hence, Median class is 20-30

So,

• l = 20

• h = 10

• f = 9

• cf = cf of preceding class = 8

• N/2 = 11

By substituting all the given values in the formula,

$\dashrightarrow\rm M= l + \Bigg \{h \times \dfrac{ \bigg( \dfrac{N}{2} - cf \bigg)}{f} \Bigg \}$

$\dashrightarrow\rm M= 20 + \Bigg \{10 \times \dfrac{ \bigg( \dfrac{22}{2} - 8 \bigg)}{9} \Bigg \}$

$\dashrightarrow\rm M= 20 + \Bigg \{10 \times \dfrac{ \bigg( 11 - 8 \bigg)}{9} \Bigg \}$

$\dashrightarrow\rm M= 20 + \Bigg \{10 \times \dfrac{3}{9} \Bigg \}$

$\dashrightarrow\rm M= 20 + \Bigg \{10 \times \dfrac{1}{3} \Bigg \}$

$\dashrightarrow\rm M= 20 + 0.33$

$\dashrightarrow\rm M= 20.33$

Additional Information :-

Mean using Direct Method :-

$\dashrightarrow\sf Mean = \dfrac{ \sum f_i x_i}{ \sum f_i}$

Mean using Short Cut Method :-

$\dashrightarrow\sf Mean =A + \dfrac{ \sum f_i d_i}{ \sum f_i}$

Mean using Step Deviation Method :-

$\dashrightarrow\sf Mean =A + \dfrac{ \sum f_i u_i}{ \sum f_i} \times h$