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# The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table:

**(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 \mathrm{~mm} $ long? Why?"

Given:

The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the given table.

To do:

We have to

(i) Draw a histogram to represent the given data.

(ii) Find whether there is any other suitable graphical representation for the same data.

(iii) Find whether it is correct to conclude that the maximum number of leaves is \( 153 \mathrm{~mm} \) long.

Solution:

(i) The data given in the question is represented in discontinuous class intervals.

To make it in the continuous class intervals, we have to subtract $0.5$ from the lower limit and add $0.5$ to the upper limit.

The modified table is as below:

S.No. | Length (in mm) | Number of leaves |

1 | 117.5-126.5 | 3 |

2 | 126.5-135.5 | 5 |

3 | 135.5-144.5 | 9 |

4 | 144.5-153.5 | 12 |

5 | 153.5-162.5 | 5 |

6 | 162.5-171.5 | 4 |

7 | 171.5-180.5 | 2 |

The histogram to represent the given data is as follows:

(ii) Yes, the data given in the question can also be represented by a frequency polygon.

(iii) No, we cannot conclude that the maximum number of leaves is $153\ mm$ long because the maximum number of leaves lies between the lengths of $144.5\ mm$ and $153.5\ mm$.

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