The table gives the frequency distribution of marks obtained by a group of students in a test.
Marks
3
4
5
6
7
8
Frequency
5
x - 1
x
9
4
1
If the mean is 5, (a) Calculate the value of x; (b) Find the : (i) mode ; (ii) median of the distribution. (c) If one of the students is selected at random, find the probability that he scored at least 7 marks.
Explanation
Marks
3
4
5
6
7
8
Frequency
5
x - 1
x
9
4
1
fx
15
4x - 4
5x
54
28
8
(b)(i) Mode = 5. (ii) Median Frequency = 18 + 2(11) = 40. Median position = 20th position = 5. (c) No of students that scored at least 7 marks = 4 + 1 = 5. Probability of scoring at least 7 marks =
