Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
Find the median of the following data: 12, 45, 12, 33, 98, 56, 22, 11, 45, 67.
33
38
45
40
38
Arrange numbers mentally in small groups or just by scanning the range (11 to 98) and locate the middle pair after writing them in ascending order.
The data set is 12, 45, 12, 33, 98, 56, 22, 11, 45, 67. Total number of observations (n) is 10.
Median=2(2nтАЛ)th┬аterm+(2nтАЛ+1)th┬аtermтАЛ
Arrange numbers mentally in small groups or just by scanning the range (11 to 98) and locate the middle pair after writing them in ascending order.
Students often forget to arrange the data in ascending order before finding the middle term, or they count n=10 as odd, applying the wrong formula for n+1/2.
Sort the data
Arrange the given data 12, 45, 12, 33, 98, 56, 22, 11, 45, 67 in ascending order: 11, 12, 12, 22, 33, 45, 45, 56, 67, 98.
11,12,12,22,33,45,45,56,67,98
Identify terms for n=10
Since n=10 (even), the median is the average of the 5th and 6th terms in the ordered list.
5th=33,6th=45
Calculate the median
Applying the formula for even number of observations, the median is the arithmetic mean of 33 and 45.
Median=233+45тАЛ=278тАЛ=38
B is correct because the average of the 5th term (33) and the 6th term (45) equals 38.
This concept is fundamental for calculating the 'Mean Deviation' in higher statistics and interpreting 'Quartiles' in data distribution charts.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download тАв 100K+ Aspirants