Two sections of Class $IX$ having $30$ students each appeared for a mathematics olympiad. The marks obtained by them are shown below:
$\begin{array}{lllllllllllllll}46 & 31 & 74 & 68 & 42 & 54 & 14 & 61 & 83 & 48 & 37 & 26 & 8 & 64 & 57 \\ 93 & 72 & 53 & 59 & 38 & 16 & 88 & 75 & 56 & 46 & 66 & 45 & 61 & 54 & 27 \\ 27 & 44 & 63 & 58 & 43 & 81 & 64 & 67 & 36 & 49 & 50 & 76 & 38 & 47 & 55 \\ 77 & 62 & 53 & 40 & 71 & 60 & 58 & 45 & 42 & 34 & 46 & 40 & 59 & 42 & 29\end{array}$
Construct a grouped frequency distribution table for the data above using the classes $0-9, 10-19$,etc.,and hence find the number of students who secured more than $49$ marks.
$\begin{array}{lllllllllllllll}46 & 31 & 74 & 68 & 42 & 54 & 14 & 61 & 83 & 48 & 37 & 26 & 8 & 64 & 57 \\ 93 & 72 & 53 & 59 & 38 & 16 & 88 & 75 & 56 & 46 & 66 & 45 & 61 & 54 & 27 \\ 27 & 44 & 63 & 58 & 43 & 81 & 64 & 67 & 36 & 49 & 50 & 76 & 38 & 47 & 55 \\ 77 & 62 & 53 & 40 & 71 & 60 & 58 & 45 & 42 & 34 & 46 & 40 & 59 & 42 & 29\end{array}$
Construct a grouped frequency distribution table for the data above using the classes $0-9, 10-19$,etc.,and hence find the number of students who secured more than $49$ marks.
(32) To construct the grouped frequency distribution,we count the number of students in each class interval:
To find the number of students who secured more than $49$ marks,we sum the frequencies of the classes $50-59, 60-69, 70-79, 80-89$,and $90-99$.
Number of students $= 12 + 10 + 6 + 3 + 1 = 32$.
| Class Interval | Frequency |
| $0-9$ | $1$ |
| $10-19$ | $2$ |
| $20-29$ | $4$ |
| $30-39$ | $6$ |
| $40-49$ | $15$ |
| $50-59$ | $12$ |
| $60-69$ | $10$ |
| $70-79$ | $6$ |
| $80-89$ | $3$ |
| $90-99$ | $1$ |
| Total | $60$ |
To find the number of students who secured more than $49$ marks,we sum the frequencies of the classes $50-59, 60-69, 70-79, 80-89$,and $90-99$.
Number of students $= 12 + 10 + 6 + 3 + 1 = 32$.
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Similar Questions
The mean of the following distribution is $50$. Find the value of $a$ and hence the frequencies of $30$ and $70$.
$x$ $f$ $10$ $17$ $30$ $5a+3$ $50$ $32$ $70$ $7a-11$ $90$ $19$
| $x$ | $f$ |
| $10$ | $17$ |
| $30$ | $5a+3$ |
| $50$ | $32$ |
| $70$ | $7a-11$ |
| $90$ | $19$ |
Difficult
View SolutionConvert the given frequency distribution into a continuous grouped frequency distribution:
Class interval Frequency $150-153$ $7$ $154-157$ $7$ $158-161$ $15$ $162-165$ $10$ $166-169$ $5$ $170-173$ $6$
In which intervals would $153.5$ and $157.5$ be included?
| Class interval | Frequency |
| $150-153$ | $7$ |
| $154-157$ | $7$ |
| $158-161$ | $15$ |
| $162-165$ | $10$ |
| $166-169$ | $5$ |
| $170-173$ | $6$ |
In which intervals would $153.5$ and $157.5$ be included?
Medium
View SolutionThe frequency distribution is given below:
Marks $0-20$ $20-40$ $40-60$ $60-100$ Number of Students $10$ $15$ $20$ $25$
This distribution has been represented graphically as shown in the image. Is this representation correct? Explain.
| Marks | $0-20$ | $20-40$ | $40-60$ | $60-100$ |
| Number of Students | $10$ | $15$ | $20$ | $25$ |
This distribution has been represented graphically as shown in the image. Is this representation correct? Explain.
Easy
View SolutionIn the class intervals $10-20$ and $20-30$,the number $20$ is included in:
Easy
View SolutionThe mean marks (out of $100$) of boys and girls in an examination are $70$ and $73$,respectively. If the mean marks of all the students in that examination is $71$,find the ratio of the number of boys to the number of girls.
Medium
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