Find the median of the following :
Number of persons in a lift : $3, 7, 6, 5, 4, 1, 7, 10, 5, 8, 7, 5, 2, 1, 10, 2, 4, 1, 4, 6, 8, 4$

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Solution

Finding median of the given data:
Given data, $3, 7, 6, 5, 4, 1, 7, 10, 5, 8, 7, 5, 2, 1, 10, 2, 4, 1, 4, 6, 8, 4$
Arranging the data in ascending order: $1, 1, 1, 2, 2, 3, 4, 4, 4, 4, 5, 5, 5, 6, 7, 7, 7, 8, 8, 10, 10$
Here number of terms, $n = 16$
We know that,
$M e d i a n = \frac{\frac{n}{2} t h t e r m + (\frac{n + 1}{2}) t h t e r m}{2} [F o r e v e n n u m b e r o f t e r m s]$
Therefore,
$\begin{array}{rcl} M e d i a n & = & \frac{\frac{22}{2} t h t e r m + (\frac{22}{2} + 1) t h t e r m}{2} \\ = & \frac{11^{t h} t e r m + 12^{t h} t e r m}{2} \\ = & \frac{5 + 5}{2} \\ = & \frac{10}{2} \\ = & 5 \end{array}$
Hence, median of the given data is $5$ .

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Find the median of the following data :

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State with reason whether following functions have inverse

(i) f: {1, 2, 3, 4} → {10} with

f = {(1, 10), (2, 10), (3, 10), (4, 10)}

(ii) g: {5, 6, 7, 8} → {1, 2, 3, 4} with

g = {(5, 4), (6, 3), (7, 4), (8, 2)}

(iii) h: {2, 3, 4, 5} → {7, 9, 11, 13} with

h = {(2, 7), (3, 9), (4, 11), (5, 13)}

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