The 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.
(N/A) The given graphical representation is incorrect.
In a histogram,the area of each rectangle is proportional to the frequency of the corresponding class interval. When class intervals are of unequal width,the heights of the rectangles must be adjusted to be proportional to the frequency density,which is defined as $\frac{\text{Frequency}}{\text{Width of class interval}}$.
Here,the class widths are:
$0-20$: width $= 20$
$20-40$: width $= 20$
$40-60$: width $= 20$
$60-100$: width $= 40$
Since the last interval $(60-100)$ has a different width,the height of the rectangle for this interval should have been adjusted to maintain the area proportionality. The current graph simply plots frequency against class intervals,which is only valid for equal class widths.
In a histogram,the area of each rectangle is proportional to the frequency of the corresponding class interval. When class intervals are of unequal width,the heights of the rectangles must be adjusted to be proportional to the frequency density,which is defined as $\frac{\text{Frequency}}{\text{Width of class interval}}$.
Here,the class widths are:
$0-20$: width $= 20$
$20-40$: width $= 20$
$40-60$: width $= 20$
$60-100$: width $= 40$
Since the last interval $(60-100)$ has a different width,the height of the rectangle for this interval should have been adjusted to maintain the area proportionality. The current graph simply plots frequency against class intervals,which is only valid for equal class widths.
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The class mark of a frequency distribution with equal sizes of two successive classes is $72$ and $77$. Then,the width of the class is ...........
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View SolutionThe following table gives the frequencies of most commonly used letters $a, e, i, o, r, t, u$ from a page of a book:
Letters $a$ $e$ $i$ $o$ $r$ $t$ $u$ Frequency $75$ $125$ $80$ $70$ $80$ $95$ $75$
Represent the information above by a bar graph.
| Letters | $a$ | $e$ | $i$ | $o$ | $r$ | $t$ | $u$ |
| Frequency | $75$ | $125$ | $80$ | $70$ | $80$ | $95$ | $75$ |
Represent the information above by a bar graph.
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View SolutionBelow is the distribution of "more than" type of marks obtained by $50$ students in a $100$ marks examination. Prepare the grouped frequency distribution from that.
Obtained marks No. of Students $0$ or more than $0$ $50$ $20$ or more than $20$ $48$ $40$ or more than $40$ $40$ $60$ or more than $60$ $31$ $80$ or more than $80$ $10$
| Obtained marks | No. of Students |
| $0$ or more than $0$ | $50$ |
| $20$ or more than $20$ | $48$ |
| $40$ or more than $40$ | $40$ |
| $60$ or more than $60$ | $31$ |
| $80$ or more than $80$ | $10$ |
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View SolutionIn a histogram, the areas of the rectangles are proportional to the frequencies. Can we say that the lengths of the rectangles are also proportional to the frequencies?
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