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