4MA0 Higher January 2018 Paper 3 Q4
4 Stephen has a biased 5-sided spinner.
He spins the spinner 80 times.
His score each time is the number that the spinner lands on.
The table shows information about his scores.
| Number on spinner | Frequency |
|---|---|
| 1 | 5 |
| 2 | 12 |
| 3 | 16 |
| 4 | 32 |
| 5 | 15 |
(a) Find Stephen’s median score. (2)
(b) Work out Stephen’s mean score. (3)
Stephen is going to spin the spinner once more.
(c) Use the information in the table to find an estimate for the probability that the spinner will land on an even number. (2)
| Scheme | Marks |
|---|---|
| \((80 + 1) \div 2\;(= 40.5(\text{th}))\) or \(80 \div 2\;(= 40(\text{th}))\) | M1 |
| 4 | A1 |
| (2) |
Notes
M1: or listing numbers and attempt to find median
| Scheme | Marks |
|---|---|
| 1×5, 2×12, 3×16, 4×32, 5×15 or 5, 24, 48, 128, 75 or 280 | M1 |
| “280” ÷ 80 | M1 |
| 3.5 oe | A1 |
| (3) |
Notes
M1: for at least 4 correct products – may be seen by side of table (products may not be evaluated);
M1: dep
Allow division by their \(\sum f\) provided addition or total under column seen
A1: condone rounding to 4 if 3.5 or 280 ÷ 80 is present
| Scheme | Marks |
|---|---|
| \(\dfrac{32}{80} + \dfrac{12}{80}\) or \(\dfrac{32 + 12}{80}\) | M1 |
| \(\dfrac{44}{80}\) | A1 |
| (2) |
Notes
M1: or for \(\dfrac{44}{n}\) where \(n > 44\) or \(\dfrac{m}{80}\) where \(m < 80\)
A1: for \(\dfrac{44}{80}\) oe or 0.55 or 55%