Calculate the median for the following distribution- begin array - c - c - WhineMarks obtained - Number of students Below 10 - 6 WhlineBelow 20 - 15 Whline Below 30 - 29 WhlineBelow 40 - 41 WhlineBelow 50 - 60 WhlineBelow 60 - 70 Whlinelendarray -4 MARKS-

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

Median for a Grouped Data

Calculate the...

Question

Calculate the median for the following distribution.

$\begin{matrix} M a r k s o b t a i n e d & N u m b e r o f s t u d e n t s B e l o w 10 & 6 B e l o w 20 & 15 B e l o w 30 & 29 B e l o w 40 & 41 B e l o w 50 & 60 B e l o w 60 & 70 \end{matrix}$ [4 MARKS]

Open in App

Solution

Concept: 1 Mark
Application: 3 Marks

The frequency distribution table from the given distribution is as follows:

$\begin{matrix} C l a s s & N u m b e r o f & C u m u l a t i v e (M a r k s o b t a i n e d) & s t u d e n t s & f r e q u e n c y (f r e q u e n c y) 0 - 10 & 6 & 6 10 - 20 & 9 & 15 20 - 30 & 14 & 29 30 - 40 & 12 & 41 40 - 50 & 19 & 60 50 - 60 & 10 & 70 \end{matrix}$

n = 70 $∴ \frac{n}{2} = 35$ . This observation lies in the class 30 - 40. So, 30 - 40 is the median class.

$∴$ l = 30, h = 10, cf = 29, f = 12

Using the formula, Median $= l + (\frac{\frac{n}{2} - c f}{f}) \times h$ , we get

Median $= 30 + (\frac{35 - 29}{12}) \times 10 = 30 + 5 = 35$

Suggest Corrections

Similar questions

Calculate the median for the following distribution.

$\begin{matrix} M a r k s o b t a i n e d & N u m b e r o f s t u d e n t s B e l o w 10 & 6 B e l o w 20 & 15 B e l o w 30 & 29 B e l o w 40 & 41 B e l o w 50 & 60 B e l o w 60 & 70 \end{matrix}$ [4 MARKS]

The following data gives the marks obtained by students in an exam.

$\begin{matrix} Class interval & Frequency B e l o w 10 & 5 B e l o w 20 & 10 B e l o w 30 & 23 B e l o w 40 & 31 B e l o w 50 & 45 B e l o w 60 & 49 \end{matrix}$

(i)Convert the cumulative distribution to a regular distribution.

(ii)Calculate the mode. [3 MARKS]

The following table gives the marks obtained by the students of a class in an exam out of 50.

$\begin{matrix} M a r k s & N o . o f S t u d e n t s B e l o w 10 & 5 B e l o w 20 & 10 B e l o w 30 & 23 B e l o w 40 & 31 B e l o w 50 & 40 \end{matrix}$

(i) Convert the cumulative frequency distribution into a regular frequency distribution.

(ii) Find the mean.

Q. Calculate the median for the following distribution.

\begin{matrix} M a r k s o b t a i n e d & N u m b e r o f s t u d e n t s B e l o w 10 & 6 B e l o w 20 & 15 B e l o w 30 & 29 B e l o w 40 & 41 B e l o w 50 & 60 B e l o w 60 & 70 \end{matrix}

Q. Question 8
For the following distribution,

\begin{matrix} M a r k s & N u m b e r o f s t u d e n t s B e l o w 10 & 3 B e l o w 20 & 12 B e l o w 30 & 27 B e l o w 40 & 57 B e l o w 50 & 75 B e l o w 60 & 80 \end{matrix}

the modal class is
(a) 10 - 20
(b) 20 - 30
(c) 30 - 40
(d) 50 - 60

Join BYJU'S Learning Program

Calculate the median for the following distribution. Marks obtainedNumber of studentsBelow 106Below 2015Below 3029Below 4041Below 5060Below 6070 [4 MARKS]

Calculate the median for the following distribution.

$\begin{matrix} M a r k s o b t a i n e d & N u m b e r o f s t u d e n t s B e l o w 10 & 6 B e l o w 20 & 15 B e l o w 30 & 29 B e l o w 40 & 41 B e l o w 50 & 60 B e l o w 60 & 70 \end{matrix}$ [4 MARKS]