The following table gives the numbers of branches and number plants in a garden of a school.
No. of branches $2$ $3$ $4$ $5$ $6$
No. of plants $14$ $21$ $28$ $20$ $17$
Calculate the mean, median and mode of the above data.

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Solution

Mean $= \frac{\sum f_{i} x_{i}}{\sum f_{i}}$
$= \frac{14 (2) + 21 (3) + 28 (4) + 20 (5) + 17 (6)}{100}$
$= \frac{28 + 63 + 112 + 100 + 102}{100}$
$= \frac{405}{100} \approx 4$
Therefore, mean of given data is approximately $4$ branches.

Since plants with $4$ branches are highest in number which is highest frequency of all the items, the modal number of branches will be $4$ .
Mode $= 4$

For a given data,
Relation between mean, mode and median is given by :
$mode = 3 \times median - 2 \times mean$
$4 = 3 \times median - 2 \times 4$
$median = 4$ .

Therefore, for the given data, mean $=$ median $=$ mode $= 4$ .

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