Question

30 observations are arranged in ascending order the values of 15th and 16 observations are P and Q find the median

Answer 1

Answer:

Median = [(n+1/2) th +(n/2 +1) th term]/2

[(30/2 )+(30/2+1)]

(15+16)/2

so hence,p+q/2

Answer 2

Answer:

The answer to the given question is the median of the 30 terms is

$\frac{(p +q )}{2}$

Step-by-step explanation:

It is given that 30 observations are arranged in ascending order.

The values of the 15th and 16 observations are P and Q

we have to find the median of the given observations.

let the total number of observations be n.

In the question, it is given that the total number of observations is 30 which is even.

Then the formula to calculate the median is

$\frac{ \frac{n}{2}th \: observation + \frac{n + 1}{2} th \: obsevation }{2}$

The terms that involve

$\frac{n}{2} is \: \frac{30}{2} = 15$

$\frac{n }{2} + 1 = \frac{30 }{2} + 1 = 15 + 1 = 16$

Therefore, the expression is

$\frac{15th \: term + 16th \: term}{2}$

It is given that the value of 15 th and 16 th terms are p and q respectively.

let's substitute the values in the formula, we get

$\frac{ p+q }{2}$

Therefore, the final answer to the given question is

$\frac{(p + q)}{2}$

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