The following data gives marks obtained by students in an exam-Marks - No- ispace of ispace students Whline Above ispace 0 - 80 Whline Above ispace 10 - 77 Whline Above ispace 20 - 72 Whline Above ispace 30 - 65 Whline Above lspace 40 - 55 Whline Above ispace 50 - 43 - Whline Above ispace 60 - 23 Mhline Above ispace 70 - 16 Whline Above ispace 80 - 10 Whline Above ispace 90 - 8 IWhline Above ispace 100 - 0 Whlinei Convert to a regular distribution-ii Find the mode- -3 MARKS-

Table: 1 Mark Formula: 1 Mark Application: 1 Mark [ Marks amp; No. of students; Above 0 amp; 80; ...

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

Byju's Answer

Standard X

Mathematics

Assumed Mean Method

The following...

Question

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

$\begin{matrix} M a r k s & N o . o f s t u d e n t s A b o v e 0 & 80 A b o v e 10 & 77 A b o v e 20 & 72 A b o v e 30 & 65 A b o v e 40 & 55 A b o v e 50 & 43 A b o v e 60 & 23 A b o v e 70 & 16 A b o v e 80 & 10 A b o v e 90 & 8 A b o v e 100 & 0 \end{matrix}$

(i) Convert to a regular distribution.

(ii) Find the mode. [3 MARKS]

Open in App

Solution

Table: 1 Mark
Formula: 1 Mark
Application: 1 Mark

$\begin{matrix} M a r k s & N o . o f s t u d e n t s A b o v e 0 & 80 A b o v e 10 & 77 A b o v e 20 & 72 A b o v e 30 & 65 A b o v e 40 & 55 A b o v e 50 & 43 A b o v e 60 & 23 A b o v e 70 & 16 A b o v e 80 & 10 A b o v e 90 & 8 A b o v e 100 & 0 \end{matrix}$

Converting to regular frequency distribution,

$\begin{matrix} C l a s s I n t e r v a l & S t u d e n t 0 - 10 & 3 10 - 20 & 5 20 - 30 & 7 30 - 40 & 10 40 - 50 & 12 50 - 60 & 20 60 - 70 & 7 70 - 80 & 6 80 - 90 & 2 90 - 100 & 8 \end{matrix}$

Modal Class is 50-60

Mode
$= I + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h$

$= 50 + \frac{20 - 12}{40 - 12 - 7} \times 10$

$= 53.81$

Suggest Corrections

Similar questions

The median class for the following data is
$\begin{matrix} M a r k s & B e l o w 10 & B e l o w 20 & B e l o w 30 & B e l o w 40 & B e l o w 50 N o . o f s t u d e n t s (c f) & 5 & 10 & 23 & 31 & 40 \end{matrix}$

Match the following

$\begin{matrix} C o l o u m n I & C o l o u m n I I I . Z n s & (P) . L i m i t i n g r a t i o = 0.414 I I . N a C l & (Q) . F r e n k e l d e f e c t I I I . C s C l & (R) . C o o r d i n a t i o n n u m b e r = 4 I V . C a F_{2} & (S) . 8 n e a r e s t n e i g h b o u r s o f t h e c a t i o n \end{matrix}$

$\begin{matrix} Trigonometric Equation & Principal Solutions 1. sin x = \frac{\sqrt{3}}{2} & A . \frac{5 π}{6} 2. tan x = \frac{- 1}{\sqrt{3}} & B . \frac{5 π}{12} 3. sec 2 x = \frac{- 2}{\sqrt{3}} & C . \frac{7 π}{12} 4. cos 3 x = (\frac{- 1}{2}) & D . \frac{π}{3} E . \frac{2 π}{9} F . \frac{4 π}{9} G . \frac{11 π}{6} H . \frac{2 π}{3} \end{matrix}$

Match the following:

$\begin{matrix} (i) & W a t e r & (A) & C o m p o u n d (i i) & H y d r o g e n & (B) & E l e m e n t (i i i) & S a l t (i v) & G o l d (v) & C a r b o n d i o x i d e (v i) & I r o n \end{matrix}$
The correct pairs are:-

The following data gives the placement statistics for a college. The annual salaries of 100 students (in lakhs) are tabulated along with the number of students in each salary bracket. Find the quartile deviation of the data to the nearest integer.

$\begin{matrix} S a l a r y B r a c k e t (i n l p a) & 0 - 5 & 5 - 10 & 10 - 15 & 15 - 20 & 20 - 25 & 25 - 30 N o . o f s t u d e n t s & 38 & 24 & 20 & 9 & 6 & 3 \end{matrix}$

Join BYJU'S Learning Program

The following data gives marks obtained by students in an exam. MarksNo. of studentsAbove 080Above 1077Above 2072Above 3065Above 4055Above 5043Above 6023Above 7016Above 8010Above 908Above 1000 (i) Convert to a regular distribution. (ii) Find the mode. [3 MARKS]