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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