The lengths of $40$ leaves of a plant are measured correct to one millimetre,and the obtained data is represented in the following table:
Length (in $mm$) Number of leaves $118-126$ $3$ $127-135$ $5$ $136-144$ $9$ $145-153$ $12$ $154-162$ $5$ $163-171$ $4$ $172-180$ $2$
$(i)$ Draw a histogram to represent the given data. [Hint: First make the class intervals continuous]
$(ii)$ Is there any other suitable graphical representation for the same data?
$(iii)$ Is it correct to conclude that the maximum number of leaves are $153 \, mm$ long? Why?
| Length (in $mm$) | Number of leaves |
| $118-126$ | $3$ |
| $127-135$ | $5$ |
| $136-144$ | $9$ |
| $145-153$ | $12$ |
| $154-162$ | $5$ |
| $163-171$ | $4$ |
| $172-180$ | $2$ |
$(i)$ Draw a histogram to represent the given data. [Hint: First make the class intervals continuous]
$(ii)$ Is there any other suitable graphical representation for the same data?
$(iii)$ Is it correct to conclude that the maximum number of leaves are $153 \, mm$ long? Why?
(N/A) $(i)$ It can be observed that the length of leaves is represented in a discontinuous class interval having a difference of $1$ between them.
Therefore,$1/2 = 0.5$ has to be added to each upper class limit and subtracted from each lower class limit to make the class intervals continuous.
Taking the length of leaves on the $x$-axis and the number of leaves on the $y$-axis,the histogram is drawn as shown in the figure.
$(ii)$ Another suitable graphical representation for this data is a frequency polygon.
$(iii)$ No,it is not correct. The maximum number of leaves $(12)$ have their lengths in the range of $144.5 \, mm$ to $153.5 \, mm$. It does not mean that all these leaves are $153 \, mm$ long.
Therefore,$1/2 = 0.5$ has to be added to each upper class limit and subtracted from each lower class limit to make the class intervals continuous.
| Length (in $mm$) | Number of leaves |
| $117.5-126.5$ | $3$ |
| $126.5-135.5$ | $5$ |
| $135.5-144.5$ | $9$ |
| $144.5-153.5$ | $12$ |
| $153.5-162.5$ | $5$ |
| $162.5-171.5$ | $4$ |
| $171.5-180.5$ | $2$ |
Taking the length of leaves on the $x$-axis and the number of leaves on the $y$-axis,the histogram is drawn as shown in the figure.
$(ii)$ Another suitable graphical representation for this data is a frequency polygon.
$(iii)$ No,it is not correct. The maximum number of leaves $(12)$ have their lengths in the range of $144.5 \, mm$ to $153.5 \, mm$. It does not mean that all these leaves are $153 \, mm$ long.
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The following table gives the life times of $400$ neon lamps:
The time (in hours) Number of lamps $300-400$ $14$ $400-500$ $56$ $500-600$ $60$ $600-700$ $86$ $700-800$ $74$ $800-900$ $62$ $900-1000$ $48$
$(i)$ Represent the given information with the help of a histogram.
$(ii)$ How many lamps have a life time of more than $700$ hours?
| The time (in hours) | Number of lamps |
| $300-400$ | $14$ |
| $400-500$ | $56$ |
| $500-600$ | $60$ |
| $600-700$ | $86$ |
| $700-800$ | $74$ |
| $800-900$ | $62$ |
| $900-1000$ | $48$ |
$(i)$ Represent the given information with the help of a histogram.
$(ii)$ How many lamps have a life time of more than $700$ hours?
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View SolutionThirty children were asked about the number of hours they watched $TV$ programmes in the previous week. The results were found as follows:
$\begin{array}{rrrrrrrrrr}1 & 6 & 2 & 3 & 5 & 12 & 5 & 8 & 4 & 8 \\ 10 & 3 & 4 & 12 & 2 & 8 & 15 & 1 & 17 & 6 \\ 3 & 2 & 8 & 5 & 9 & 6 & 8 & 7 & 14 & 12\end{array}$
$(i)$ Make a grouped frequency distribution table for this data,taking class width $5$ and one of the class intervals as $5-10$.
$(ii)$ How many children watched television for $15$ or more hours a week?
$\begin{array}{rrrrrrrrrr}1 & 6 & 2 & 3 & 5 & 12 & 5 & 8 & 4 & 8 \\ 10 & 3 & 4 & 12 & 2 & 8 & 15 & 1 & 17 & 6 \\ 3 & 2 & 8 & 5 & 9 & 6 & 8 & 7 & 14 & 12\end{array}$
$(i)$ Make a grouped frequency distribution table for this data,taking class width $5$ and one of the class intervals as $5-10$.
$(ii)$ How many children watched television for $15$ or more hours a week?
Medium
View SolutionThe following number of goals were scored by a team in a series of $10$ matches:
$2, 3, 4, 5, 0, 1, 3, 3, 4, 3$
Find the mean,median,and mode of these scores.
$2, 3, 4, 5, 0, 1, 3, 3, 4, 3$
Find the mean,median,and mode of these scores.
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View SolutionLet us consider the following frequency distribution table which gives the weights of $38$ students of a class:
Weights (in $kg$) Number of students $31-35$ $9$ $36-40$ $5$ $41-45$ $14$ $46-50$ $3$ $51-55$ $1$ $56-60$ $2$ $61-65$ $2$ $66-70$ $1$ $71-75$ $1$ Total $38$
If two new students of weights $35.5\, kg$ and $40.5\, kg$ are admitted to this class,how should the frequency distribution table be adjusted to include them?
| Weights (in $kg$) | Number of students |
| $31-35$ | $9$ |
| $36-40$ | $5$ |
| $41-45$ | $14$ |
| $46-50$ | $3$ |
| $51-55$ | $1$ |
| $56-60$ | $2$ |
| $61-65$ | $2$ |
| $66-70$ | $1$ |
| $71-75$ | $1$ |
| Total | $38$ |
If two new students of weights $35.5\, kg$ and $40.5\, kg$ are admitted to this class,how should the frequency distribution table be adjusted to include them?
Difficult
View SolutionThree coins were tossed $30$ times simultaneously. Each time the number of heads occurring was noted down as follows:
$\begin{array}{llllllllll}0 & 1 & 2 & 2 & 1 & 2 & 3 & 1 & 3 & 0 \\ 1 & 3 & 1 & 1 & 2 & 2 & 0 & 1 & 2 & 1 \\ 3 & 0 & 0 & 1 & 1 & 2 & 3 & 2 & 2 & 0\end{array}$
Prepare a frequency distribution table for the data given above.
$\begin{array}{llllllllll}0 & 1 & 2 & 2 & 1 & 2 & 3 & 1 & 3 & 0 \\ 1 & 3 & 1 & 1 & 2 & 2 & 0 & 1 & 2 & 1 \\ 3 & 0 & 0 & 1 & 1 & 2 & 3 & 2 & 2 & 0\end{array}$
Prepare a frequency distribution table for the data given above.
Easy
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