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.
Mode = 7, Number of students scoring above average = 4
The data are the 9 marks: 5, 8, 7, 9, 6, 7, 8, 7, 10.
The mode is the value occurring most often. Counting, 7 appears three times while 8 appears twice and the rest once, so the mode = 7.
The average (mean) = \(\dfrac{5+8+7+9+6+7+8+7+10}{9}\).
The sum is \(67\), so the mean = \(\tfrac{67}{9} \approx 7.44\).
Now count the marks strictly greater than 7.44: these are 8, 9, 8 and 10.
That is 4 students scoring above the average.
The key idea is that mode is the most frequent value while 'above average' is compared against the mean, not the mode. Hence Mode = 7, Number of students scoring above average = 4.
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 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 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 ?
