Class 9

Math

All topics

Statistics

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 $153mm$ long? Why?

Length (in mm) | New length(in mm) | No. of leaves |

118 - 126 | 117.5 - 126.5 | 3 |

127 - 135 | 126.5 - 135.5 | 5 |

136 - 144 | 135.5 - 144.5 | 9 |

145 - 153 | 144.5 - 153.5 | 12 |

154 - 162 | 153.5 - 162.5 | 5 |

163 - 171 | 162.5 - 171.5 | 4 |

172 - 180 | 171.5 - 180.5 | 2 |

In order to make a histogram, we need to convert discontinuous classes to continuous classes.

Adjustment = \dfrac 12 (\mbox {lower limit of class - upper limit of previous class)}

$=21 (127−126)=0.5$

So, $0.5$ needs to be subtracted from upper limit of previous class and lower limit of next class.

(iii) No. It is a range. The maximum number of leaves lies in between $144.5mm−154.5mm$. Not necessary that it all occurs as $153mm$ length.