The table shows the distribution of marks scored by some students in a test. (a) If the mean mark is , find the value of m. (b) Find the : (i) interquartile range (ii) probability of selecting a student who scored at least 4 marks in the test.
Explanation
Mark (x)
1
2
3
4
5
Total
Frequency (f)
m + 2
m - 1
2m - 3
m + 5
3m - 4
8m - 1
fx
m + 2
2m - 2
6m - 9
4m + 20
15m - 20
28m - 9
(a) Mean (b)(i) Interquartile range = Third quartile - First quartile Frequency = 8(3) - 1 = 24 - 1 = 23 position = 4 position = 2 Interquartile range : 4 - 2 = 2 (ii) P(at least 4 marks) = = =
