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# Ex.14.2 Q4 Statistics Solution - NCERT Maths Class 9

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## Question

The heights of $$50$$ students, measured to the nearest centimeters, have been found to be as follows:

$$161\,\,\,\, 150\,\,\,\, 154\,\,\,\, 165\,\,\,\, 168\,\,\,\, 161\,\,\,\, 154\,\,\,\, 162\,\,\,\, \\150\,\,\,\, 151\,\,\,\,162\,\,\,\, 164\,\,\,\, 171\,\,\,\, 165\,\,\,\, 158\,\,\,\, 154\,\,\,\,\\ 156\,\,\,\, 172\,\,\,\, 160\,\,\,\, 170\,\,\,\, 153\,\,\,\, 159\,\,\,\, 161\,\,\,\, 170\,\,\,\,\\ 162\,\,\,\, 165\,\,\,\, 166\,\,\,\, 168\,\,\,\, 165\,\,\,\,164\,\,\,\, 154\,\,\,\, 152\,\,\,\,\\ 153\,\,\,\, 156\,\,\,\, 158\,\,\,\, 162\,\,\,\, 160\,\,\,\, 161\,\,\,\, 173\,\,\,\, 166 \,\,\,\,\\161\,\,\,\, 159\,\,\,\, 162\,\,\,\, 167\,\,\,\, 168\,\,\,\, 159\,\,\,\, 158\,\,\,\, 153\,\,\,\,\\ 154\,\,\,\, 159$$

1. Represent the data given above by a grouped frequency distribution table,Taking the class intervals as $$(160 – 165), (165 – 170),$$ etc.
2. What can you conclude about their heights from the table?

Video Solution
Statistics
Ex exercise-14-2 | Question 4

## Text Solution

What is known?

• The heights of $$50$$ students in $$\rm cm.$$
• Class size is $$5$$ [from the given instruction of class intervals to be taken as $$160- 165, 165-170, 170-175$$ …. and so on].

What is unknown?

• Constructing a grouped frequency distribution table.
• Making inferences and drawing conclusions from the data of “heights of students”.

Reasoning:

According to class interval we can check how many numbers lie in between , like this we can draw frequency distribution table and can be conclude about height from table.

Steps:

A grouped frequency distribution table with a class size of $$5,$$ for the heights of $$50$$ students can be constructed as follows:

 Height (in cm) Number of Students (frequency) $$150-155$$ $$12$$ $$155-160$$ $$9$$ $$160-165$$ $$14$$ $$165-170$$ $$10$$ $$170-175$$ $$5$$ Total $$50$$

Since ‘$$150$$’ is the lowest value, we started the $$1\rm st$$ class interval at $$150.$$

The following features / conclusions can be drawn from the table:

• A majority of $$70\%$$ of the students ($$35$$ students) are below $$165\rm cm$$ height.
• Only a $$10\%$$ of the students ($$5$$ students) are at a height of $$170\rm cm$$ or above.

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