Foundation June 2024 Paper 2 Q28
28 The table shows information about the weights of 120 oranges.
| Weight (\(w\) grams) | Frequency |
|---|---|
| \(50 \lt w \leqslant 100\) | 34 |
| \(100 \lt w \leqslant 150\) | 29 |
| \(150 \lt w \leqslant 200\) | 27 |
| \(200 \lt w \leqslant 250\) | 19 |
| \(250 \lt w \leqslant 300\) | 11 |
(a) Find the class interval that contains the median. (1)
(b) Calculate an estimate for the mean weight of the 120 oranges.
Give your answer correct to 3 significant figures. (3)
Give your answer correct to 3 significant figures. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(100 \lt w \leqslant 150\) | B1 | cao |
| Answer | Mark | Mark scheme |
|---|---|---|
| 152 | M1 | for finding 5 products within the interval (including end points) with not more than one error, may be seen near table, eg \(75 \times 34\ (= 2550)\), \(125 \times 29\ (= 3625)\), \(175 \times 27\ (= 4725)\), \(225 \times 19\ (= 4275)\), \(275 \times 11\ (= 3025)\) or for 18200 |
| M1 | for \(\Sigma fx \div \Sigma f\) eg \((\text{``}2550\text{''} + \text{``}3625\text{''} + \text{``}4725\text{''} + \text{``}4275\text{''} + \text{``}3025\text{''}) \div 120\) or \(\text{``}18200\text{''} \div 120\) | |
| A1 | for answer in the range 151 to 152 |
Additional guidance
do not award this mark if the final answer comes from an alternative incorrect method, eg \(120 \div 5\ (= 24)\)
or \(\Sigma mp \div \Sigma f\ (875 \div 120\ (= 7.29\ldots))\)
or \(\Sigma mp \div 5\ (875 \div 5\ (= 175))\)
| Min \(fx\) | Max \(fx\) |
|---|---|
| 1700 | 3400 |
| 2900 | 4350 |
| 4050 | 5400 |
| 3800 | 4750 |
| 2750 | 3300 |
| 15200 | 21200 |
\(\Sigma fx\) must come from 5 products,
\(fx\) within intervals (including end points)
Correct midpoints must be used for the award of the A mark