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
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.
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:
Since the number of observations (n) is an even number (10), the second formula will be used.
Substituting the respective values in the formula,
Therefore, x = 62.