A spinner is numbered 1, 2, 3, 4 and 5.
Rinesh spins the spinner many times.
He works out the relative frequency that the spinner lands on each number.
(a) Complete the table.
(b) Rinesh spins the spinner another 1500 times.
Calculate the expected number of times the spinner lands on 2.
Most-appropriate topic codes (Cambridge IGCSE Mathematics 0580):
(a)
The sum of all relative frequencies must be 1.
$1 – (0.15 + 0.22 + 0.26 + 0.25)$
$1 – 0.88 = 0.12$
✅ Answer: 0.12
(b)
Multiply the expected probability of landing on 2 by the total number of spins.
$\text{Expected times} = 0.22 \times 1500$
$\text{Expected times} = 330$
✅ Answer: 330
Olga owns a fruit and vegetable shop.
(a) An apple weighs 70 g correct to the nearest 5g.
Complete the statement about the mass, m grams, of this apple.
(b) The number of strawberries in each of 12 boxes is shown below.
23 21 21 20 21 20
22 22 21 20 20 20
(i) Find the range.
(ii) Write down the mode.
(iii) Find the median.
(iv) Calculate the mean.
(v) Find the probability that a box chosen at random has 22 or 23 strawberries in the box.
(c) The shop sells potatoes in bags A, B and C.
(d) The price of plums is $2.40 per kilogram.
Olga reduces this price by 35%.
Calculate the new price per kilogram.
(a) Ans: 67.5 ≤ m < 72.5
For rounding to nearest 5g, the lower bound is 70-2.5=67.5g and upper bound is 70+2.5=72.5g.
(b)
(i) Ans: 3 → Range = Max(23) – Min(20) = 3
(ii) Ans: 20 → Mode is most frequent value (appears 5 times)
(iii) Ans: 21 → Median of 12 values is average of 6th and 7th when ordered
(iv) Ans: 20.92 → Mean = (23+21+…+20)/12 = 251/12 ≈ 20.92
(v) Ans: ¼ → Probability = (2 boxes of 22 + 1 of 23)/12 = 3/12 = ¼
(c) Ans: Bag B
Comparing value for money by calculating price per kg shows Bag B is cheapest.
(d) Ans: $1.56
New price = $2.40 – (35% of $2.40) = $2.40 × 0.65 = $1.56
