- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
The lengths of 40 leaves of a plant are measured correct to nearest millimetre, and the data obtained is represented in the following table:
Length (in mm): | 118-126 | 127-135 | 136-144 | 145-153 | 154-162 | 163-171 | 172-180 |
No. of leaves: | 3 | 5 | 9 | 12 | 5 | 4 | 2 |
Find the median length of the leaves.
(Hint: The data needs to be converted to continuous classes for finding the median since the formula assumes continuous classes. The classes then change to 117.5 – 126.5
Given:
The lengths of 40 leaves of a plant are n measured correct to the nearest millimetre.
To do:
We have to find the mean length of the leaf.
Solution:
Arranging the classes in exclusive form and then forming its cumulative frequency table as below, we get,
Here,
$N = 40$
$\frac{N}{2} = \frac{40}{2} = 20$
The cumulative frequency just greater than $\frac{N}{2}$ is 29 and the corresponding class is 144.5 – 153.5.
This implies, that 144.5 – 153.5 is the median class.
Therefore,
$l = 144.5, f = 12, F = 17$ and $h = (153.5 - 144.5) = 9$
Median $=\mathrm{l}+\frac{\frac{\mathrm{N}}{2}-\mathrm{F}}{\mathrm{f}} \times \mathrm{h}$
$=144.5+\frac{20-17}{12} \times 9$
$=144.5+\frac{3}{4} \times 3$
$=144.5+\frac{9}{4}$
$= 144.5 + 2.25$
$= 146.75$
The mean length of the leaf is 146.75 mm.