The following table shows the distribution of test scores in a class.
Scores
1
2
3
4
5
7
8
9
10
No of pupils
1
1
5
3
\(k^{2}+ 1\)
6
2
3
4
(a) If the mean score of the class is 6, find the : (i) value of k (ii) median score.
(b) Draw a bar chart for the distribution.
(c) If a pupil is picked at random, what is the probability that he/ she will score less than 6?
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
Scores (x)
1
2
3
4
5
7
8
9
10
Total
No of pupils (f)
1
1
5
3
\(k^{2} + 1\)
6
2
3
4
\(k^{2} + 26\)
fx
1
2
15
12
\(5k^{2} + 5\)
42
16
27
40
\(5k^{2} + 160\)
\(\bar{x} = \frac{\sum fx}{\sum f}\)
\(6 = \frac{5k^{2} + 160}{k^{2} + 26}\)
\(6(k^{2} + 26) = 5k^{2} + 160\)
\(6k^{2} + 156 = 5k^{2} + 160\)
\(6k^{2} - 5k^{2} = 160 - 156\)
\(k^{2} = 4\)
\( k = \sqrt{4} = 2\)
\(\therefore k = 2\)
(ii) \(Median = \frac{5 + 7}{2}\)
= \(\frac{12}{2} = 6\)
(b)
(c) Probability of scoring less than 6 = \(\frac{15}{30} \)
= \(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #53050)