Math, asked by nayana825, 11 months ago

2. The following
following data have been arranged in
cending order. If their median is 63, find the
value of x.
34, 37, 53, 55, X, X + 2, 77, 83, 89 and 100.

Answers

Answered by Anonymous
79

Solution :-

Data which is arranged in ascending order = 34, 37, 53, 55, x, x + 2, 77, 83, 89, 100

Number of observations n = 10 (even)

So, Median = Average of (n/2)th observation and (n/2 + 1)th observation

⇒ Median = Average of (10/2)th observation and (10/2 + 1)th observation

⇒ Median = Average of 5th and 6th observations

⇒ Median = Average of x and (x + 2)

⇒ Median = (x + x + 2)/2

⇒ Median = (2x + 2)/2

⇒ Median = x + 1

Also, Median = 63

⇒ x + 1 = 63

⇒ x = 63 - 1

⇒ x = 62

Therefore the value of x is 62.

Answered by Equestriadash
58

Given: Data arranged in ascending order and the median.

To find: The value of x.

Answer:

Data: 34, 37, 53, 55, x, x + 2, 77, 83, 89 and 100.

Median: 63

Formula to find the median:

\tt When\ n\ (the\ number\ of\ observations)\ is\ an\ odd\ number,\\ \\\\\implies\ \bigg(\dfrac{n\ +\ 1}{2}\bigg)th\ term.\\\\\\When\ n\ is\ an\ even\ number,\\\\\\\implies\ \dfrac{\bigg[\bigg(\dfrac{n}{2}\bigg)\ +\ \bigg(\dfrac{n}{2}\ +\ 1\bigg)\bigg]}{2}\ th\ term.

Since the number of observations (n) is an even number (10), the second formula will be used.

Substituting the respective values in the formula,

\tt 63\ =\ \dfrac{\bigg[\bigg(\dfrac{10}{2}\bigg)\ +\ \bigg(\dfrac{10}{2}\ +\ 1\bigg)\bigg]}{2}\ th\ term\\  \\\\63\ =\ \dfrac{\bigg[5th\ +\ 6th\bigg]}{2}\ term\\\\\\63\ =\ \dfrac{x\ +\ x\ +\ 2}{2}\\\\\\63\ =\ \dfrac{\bigg[2x\ +\ 2\bigg]}{2}\\\\\\63\ =\ x\ +\ 1\\\\\\63\ -\ 1\ =\ x\\\\\\62\ =\ x

Therefore, x = 62.


Anonymous: Awesome
Equestriadash: Thank you! ^_^"
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