Question

median of an ungrouped data 13, 10, 12, 18, 17,p is observed as 14.find P by giving reasons

Answer 1

Solution :-

First we will arrange this data in ascending order.

10, 12, 13, P, 17, 18

P is written after 13 and before 17 while arranging the data in ascending order because median of the given data is 14.

In the given data, the total number of observations are 6.

So, if 'n' is even, then mean of middle two numbers will be the median of the data.

⇒ Median = [(n + 1)/2]th item

⇒ [(6 + 1)/2]th item

⇒ (7/2)th item

⇒ Median = 3.5th item or (3rd item+ 4th item)/2

⇒ 14 = (13 + P)/2 

⇒ 13 + P = 14*2

⇒ 13 + P = 28

⇒ P = 28 - 13

⇒ P =15

So, the value of P is 15

Answer.

Answer 2

The value of p is 15 .

Step-by-step explanation:

Given data:

13, 10, 12, 18, 17, p

Median = 14

To find the value of p:

Write the data in the ascending order (smallest to largest).

p is written after 13 and before 17 while arranging the data in ascending order because median of the given data is 14.

10, 12, 13, p, 17, 18

Number of observation (N) = 6

If N is even, then

$\text{Median} =\left( \frac{N+1}{2}\right)^{th} \text{value}$

$14=\left( \frac{6+1}{2}\right)^{th} \text{value}$

$14=\left( \frac{7}{2}\right)^{th} \text{value}$

$14=3.5^{th} \ \text{value}$

Median = 3.5th value (or) $\frac{3^{rd} + 4^{th}}{2} \text{value}$

In ascending order, 3rd value 13 and 4th value p.

$14=\left(\frac{13+p}{2} \right)$

28 = 13 + p

28 – 13 = p

15 = p

p = 15

The value of p is 15 .

To learn more...

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