The heights of $50$ students,measured to the nearest centimetres,have been found to be as follows:
$\begin{array}{llllllllll}161 & 150 & 154 & 165 & 168 & 161 & 154 & 162 & 150 & 151 \\ 162 & 164 & 171 & 165 & 158 & 154 & 156 & 172 & 160 & 170 \\ 153 & 159 & 161 & 170 & 162 & 165 & 166 & 168 & 165 & 164 \\ 154 & 152 & 153 & 156 & 158 & 162 & 160 & 161 & 173 & 166 \\ 161 & 159 & 162 & 167 & 168 & 159 & 158 & 153 & 154 & 159\end{array}$
$(i)$ Represent the data given above by a grouped frequency distribution table,taking the class intervals as $150-155, 155-160,$ etc.
$(ii)$ What can you conclude about their heights from the table?
$\begin{array}{llllllllll}161 & 150 & 154 & 165 & 168 & 161 & 154 & 162 & 150 & 151 \\ 162 & 164 & 171 & 165 & 158 & 154 & 156 & 172 & 160 & 170 \\ 153 & 159 & 161 & 170 & 162 & 165 & 166 & 168 & 165 & 164 \\ 154 & 152 & 153 & 156 & 158 & 162 & 160 & 161 & 173 & 166 \\ 161 & 159 & 162 & 167 & 168 & 159 & 158 & 153 & 154 & 159\end{array}$
$(i)$ Represent the data given above by a grouped frequency distribution table,taking the class intervals as $150-155, 155-160,$ etc.
$(ii)$ What can you conclude about their heights from the table?
(N/A) $(i)$ $A$ grouped frequency distribution table is constructed by taking class intervals of size $5$ starting from $150$. By tallying the data provided,we obtain the following frequency distribution table:
$(ii)$ From the table,it can be concluded that $35$ students (i.e.,$12+9+14 = 35$) have a height less than $165\, cm$. Since $35/50 = 70\%$,we can conclude that $70\%$ of the students are shorter than $165\, cm$.
| Height (in $cm$) | Number of students (frequency) |
| $150-155$ | $12$ |
| $155-160$ | $9$ |
| $160-165$ | $14$ |
| $165-170$ | $10$ |
| $170-175$ | $5$ |
| Total | $50$ |
$(ii)$ From the table,it can be concluded that $35$ students (i.e.,$12+9+14 = 35$) have a height less than $165\, cm$. Since $35/50 = 70\%$,we can conclude that $70\%$ of the students are shorter than $165\, cm$.
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Find the mean salary of $60$ workers of a factory from the following table:
Salary (in Rs.) Number of workers $3000$ $16$ $4000$ $12$ $5000$ $10$ $6000$ $8$ $7000$ $6$ $8000$ $4$ $9000$ $3$ $10000$ $1$ Total $60$
| Salary (in Rs.) | Number of workers |
| $3000$ | $16$ |
| $4000$ | $12$ |
| $5000$ | $10$ |
| $6000$ | $8$ |
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| $10000$ | $1$ |
| Total | $60$ |
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View SolutionThe following observations have been arranged in ascending order. If the median of the data is $63$,find the value of $x.$
$29, 32, 48, 50, x, x+ 2, 72, 78, 84, 95$
$29, 32, 48, 50, x, x+ 2, 72, 78, 84, 95$
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View SolutionFind the mode of the following marks (out of $10$) obtained by $20$ students:
$4, 6, 5, 9, 3, 2, 7, 7, 6, 5, 4, 9, 10, 10, 3, 4, 7, 6, 9, 9$
$4, 6, 5, 9, 3, 2, 7, 7, 6, 5, 4, 9, 10, 10, 3, 4, 7, 6, 9, 9$
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View SolutionThe relative humidity (in $\%$) of a certain city for a month of $30$ days was as follows:
$98.1$ $98.6$ $99.2$ $90.3$ $86.5$ $95.3$ $92.9$ $96.3$ $94.2$ $95.1$ $89.2$ $92.3$ $97.1$ $93.5$ $92.7$ $95.1$ $97.2$ $93.3$ $95.2$ $97.3$ $96.2$ $92.1$ $84.9$ $90.2$ $95.7$ $98.3$ $97.3$ $96.1$ $92.1$ $89$
$(i)$ Construct a grouped frequency distribution table with classes $84-86, 86-88$,etc.
$(ii)$ Which month or season do you think this data is about?
$(iii)$ What is the range of this data?
| $98.1$ | $98.6$ | $99.2$ | $90.3$ | $86.5$ | $95.3$ | $92.9$ | $96.3$ | $94.2$ | $95.1$ |
| $89.2$ | $92.3$ | $97.1$ | $93.5$ | $92.7$ | $95.1$ | $97.2$ | $93.3$ | $95.2$ | $97.3$ |
| $96.2$ | $92.1$ | $84.9$ | $90.2$ | $95.7$ | $98.3$ | $97.3$ | $96.1$ | $92.1$ | $89$ |
$(i)$ Construct a grouped frequency distribution table with classes $84-86, 86-88$,etc.
$(ii)$ Which month or season do you think this data is about?
$(iii)$ What is the range of this data?
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