The following table gives the number of branches and number of plants in the garden of a school.
No. of branches ($x$): | 2 | 3 | 4 | 5 | 6 |
No. of plants ($f$): | 49 | 43 | 57 | 38 | 13 |
Calculate the average number of branches per plant.
Given:
The number of branches and number of plants in the garden of a school.
To do:
We have to calculate the average number of branches per plant.
Solution:
Let the assumed mean be $A=4$
Number of branches ($x_i$) | Number of plants ($f_i$) | $d_i =x_i -A$ $A=4$ | $f_i \times\ d_i$ |
2 | 49 | $-2$ | $-98$ |
3 | 43 | $-1$ | $-43$ |
4-$A$ | 57 | 0 | 0 |
5 | 38 | 1 | 38 |
6 | 13 | 2 | 26 |
Total | $\sum{f_i}=200$ | | $\sum{f_id_i}=-77$ |
We know that,
Mean $=A+\frac{\sum{f_id_i}}{\sum{f_i}}$
Therefore,
Mean $=4+(\frac{-77}{200})$
$=4-0.385$
$=3.615$
The average number of branches per plant is $3.615$.
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