The table shows the scores obtained when a fair... | WAEC SSCE - General Mathematics - 2011

Question 1 Report

The table shows the scores obtained when a fair die was thrown a number of times.

Score	1	2	3	4	5	6
Frequency	2	5	x	11	9	10

If the probability of obtaining a 3 is 0.26, find the (a) median

(b) standard deviation of the distribution.

Answer

Score	1	2	3	4	5	6
Frequency	2	5	x	11	9	10

Find x. Total \(N=37+x\). Since \(P(3)=0.26\):

\[ \frac{x}{37+x}=0.26 \Rightarrow x=9.62+0.26x \Rightarrow 0.74x=9.62 \Rightarrow x=13 \]

So frequencies are \(2,5,13,11,9,10\) with \(N=50\).

(a) Median. With \(N=50\), the median is the mean of the 25th and 26th values. Cumulative frequencies: 2, 7, 20, 31, ... Both the 25th and 26th fall at score 4, so median = 4.

(b) Standard deviation. First the mean:

\[ \Sigma fx = 2+10+39+44+45+60 = 200,\quad \bar{x}=\frac{200}{50}=4 \] \[ \Sigma fx^2 = 2+20+117+176+225+360 = 900 \] \[ \text{Variance}=\frac{\Sigma fx^2}{N}-\bar{x}^2=\frac{900}{50}-4^2=18-16=2 \] \[ \text{SD}=\sqrt{2}\approx 1.41 \]

Read lesson note on Probability (WAEC)

Answer Details

Score	1	2	3	4	5	6
Frequency	2	5	x	11	9	10

Find x. Total \(N=37+x\). Since \(P(3)=0.26\):

\[ \frac{x}{37+x}=0.26 \Rightarrow x=9.62+0.26x \Rightarrow 0.74x=9.62 \Rightarrow x=13 \]

So frequencies are \(2,5,13,11,9,10\) with \(N=50\).

(a) Median. With \(N=50\), the median is the mean of the 25th and 26th values. Cumulative frequencies: 2, 7, 20, 31, ... Both the 25th and 26th fall at score 4, so median = 4.

(b) Standard deviation. First the mean:

Read lesson note on Probability (WAEC)

Probability

View Answer

The table shows the scores obtained when a fair die was thrown a number of times. Score 1 2 3 4 5 6 Frequency 2 5 x 11 9 10 If the probability of obtaining ...

Download The App On Google Playstore

The table shows the scores obtained when a fair die was thrown a number of times. Score 1 2 3 4 5 6 Frequency 2 5 x 11 9 10 If the probability of obtaining ...

Related Questions

Download The App On Google Playstore