The marks of 9 students are: 16, 20, 24, 27, 31, 36, 39, 42, 48. If the marks of the student who scored 48 are replaced by 52, what is the value of the new median?
31
For an odd number n of observations arranged in ascending order, the median is the \(\left(\frac{n + 1}{2}\right)\)th observation.
Here n = 9, so the median is the \(\frac{9 + 1}{2} = 5\)th observation.
After replacing 48 by 52, the marks in ascending order are 16, 20, 24, 27, 31, 36, 39, 42, 52; the largest value only changed, so the order of the first eight values is unaffected.
Therefore the new median is the 5th value, 31.
Check: in 16, 20, 24, 27, 31, 36, 39, 42, 52 there are four values (16, 20, 24, 27) below 31 and four values (36, 39, 42, 52) above it, so 31 is the middle value.
Hence, 31.
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Important Questions from Measures of Central Tendency
A random sample of 20 people is classified in the following table according to their ages:
Age
Frequency
15 – 25
2
25 – 35
4
35 – 45
6
45 – 55
5
55 - 65
3
What is the mean age of this group of people?
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If the difference of mode and median is 36, then the difference of median and mean is:
In a Mathematics test 15 students scored 80 marks, 20 students scored 75 marks, 28 students scored 65 marks and 25 students scored 60 marks, mode of the score is:
If the mode of the scores 10, 12, 13, 15, 15, 13, 12, 10, x is 15, then what is the value of x?
