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 use the median formula for continuous classes.
Total frequency \(N = 5+8+6+6+5 = 30\), so \(\tfrac{N}{2} = 15\).
Cumulative frequencies are 5, 13, 19, 25, 30. The value 15 first exceeds a cumulative total in the 20-30 class, so that is the median class.
For that class the lower boundary \(l = 20\), width \(h = 10\), frequency \(f = 6\), and the preceding cumulative frequency \(cf = 13\).
Median = \(l + \dfrac{\tfrac{N}{2} - cf}{f}\times h\).
Substitute: \(20 + \dfrac{15 - 13}{6}\times 10 = 20 + \tfrac{2}{6}\times 10 = 20 + 3.33\).
So the median \(= 23.33\).
The key idea is locating the median class through cumulative frequency, then interpolating within it. The median is 23.3.
Similar Questions
The given table shows the number of people in different age groups. Find the mean age of the given number of people.
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 The marks obtained by 9 students in a test are: 5, 8, 7, 9, 6, 7, 8, 7, 10.
Determine: (i) Mode of the marks, (ii) Number of students scoring above average.
If the mode of the data set {a, a + 2, a + 4, a + 6, a + 6, a + 6, a + 8} is 26, find a.
The given table shows the number of people in different age groups. Find the mean age of the given number of people.
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.
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 The marks obtained by 9 students in a test are: 5, 8, 7, 9, 6, 7, 8, 7, 10. Determine: (i) Mode of the marks, (ii) Number of students scoring above average.
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 ?
