If the marks scored by the students in a class test out of 50 then, Find the Median of the following data:Marks Frequency 0-10 5 10-20 8 20-30 6 30-40 6 40-50 5
23.3
This is a grouped-frequency distribution, so the median is found using the median-class formula, not by simply ordering values.
First find the total frequency: \(N=5+8+6+6+5=30\), so \(\frac{N}{2}=15\).
Build the cumulative frequencies class by class: 5, then 5+8=13, then 13+6=19, then 19+6=25, then 25+5=30.
The median class is the one whose cumulative frequency first reaches or crosses 15. Since 13 < 15 ≤ 19, the class 20-30 is the median class.
For this class the values are: lower boundary \(l=20\), frequency \(f=6\), cumulative frequency before it \(cf=13\), and class width \(h=10\).
Apply \(\text{Median}=l+\frac{\frac{N}{2}-cf}{f}\times h=20+\frac{15-13}{6}\times 10=20+\frac{2}{6}\times 10\).
This gives \(20+3.33=23.33\). The formula linearly interpolates within the median class using the position N/2. Hence the median of the data is 23.3.
Similar Questions
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If the mode of the data set {a, a + 2, a + 4, a + 6, a + 6, a + 6, a + 8} is 26, find a.
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Class interval of age (in years) Number of people (f) 25 - 29 10 30 - 34 12 35 - 39 8 40 - 44 5 45 - 49 15 50 - 54 10 55 - 59 15 If the mode of the data set {a, a + 2, a + 4, a + 6, a + 6, a + 6, a + 8} is 26, find a.
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Important Questions from Statistics
The mean and variance of five observations are 14 and 13.2 respectively. Three of the five observations are 11, 16 and 20. What are the other two observations ?
A die is thrown 10 times and obtained the following outputs :
1, 2, 1, 1, 2, 1, 4, 6, 5, 4
What will be the mode of data so obtained ?
Consider the following frequency distribution :
x 1 2 3 5 f 4 6 9 7 What is the value of median of the distribution ?
For data -1, 1, 4, 3, 8, 12, 17, 19, 9, 11; if M is the median of first 5 observations and N is the median of last five observations, then what is the value of 4M - N ?
Let P, Q, R represent mean, median and mode. If for some distribution \(5 P=4 Q=\frac{R}{2}\) then what is \(\frac{P+Q}{2 P+0.7 R}\) equal to ?
