CIE iGCSE Maths C9.3 Averages and range Exam Style Practice Questions- Paper 1
Question
A delivery driver records the number of pizzas she delivers each month for one year.
(a) Complete the stem-and-leaf diagram.
(b) Find the median.
▶️Answer/Explanation
>(a)
(b) 46
split the numbers into stems (tens digits) and leaves (ones digits).
- 20s: 22, 28
- 30s: 36, 39
- 40s: 41, 44, 48, 49
- 50s: 52, 54, 57, 57
(b)
To find the median, order the data
$
22, 28, 36, 39, 41, 44, 48, 49, 52, 54, 57, 57
$
There are 12 data points, so the median is the average of the 6th and 7th values
$
\frac{44 + 48}{2} = \frac{92}{2} = 46
$
Question
The range of eight numbers is 31.
These are seven of the numbers.
28 36 42 24 38 16 21
Find the two possible values of the eighth number.
▶️Answer/Explanation
11, 47
- Minimum value = 16
- Maximum value = 42
$\text{Range} = \text{Maximum number} – \text{Minimum number}$
If the 8th number is the new maximum, the range becomes
$\text{New maximum} – 16 = 31$
$\text{New maximum} = 31 + 16 = 47$
So, the 8th number could be 47.
If the 8th number is the new minimum, the range becomes
$42 – \text{New minimum} = 31$
$\text{New minimum} = 42 – 31 = 11$
So, the 8th number could be 11.
Question
Sarah records the number of people who play golf on each of 14 days.
(a) Complete the stem-and-leaf diagram.
(b) Find the median.
▶️Answer/Explanation
(a)
(b) 61
The data:
28, 46, 54, 71, 70, 65, 49, 50, 64, 77, 68, 72, 45, 58
Arranged in order:
$
28, 45, 46, 49, 50, 54, 58, 64, 65, 68, 70, 71, 72, 77
$
(b)
there are 14 numbers, the median is the average of the 7th and 8th values.
The 7th number is 58, and the 8th number is 64.
$
\text{Median} = \frac{58 + 64}{2} = \frac{122}{2} = 61
$
Question
13 17 13 17 19 13 31 21 29
(a) For the numbers above, find
(i) the range,
(ii) the median.
(b) Write down the only number in the list which is not a prime number.
Answer/Explanation
(a)(i) 18
(ii)
(b)21
Answer/Explanation
Ans:
(b) Write down the only number in the list which is not a prime number.
Answer/Explanation
Ans: 21
Question
8 15 7 8 7 15 4 13 4 3 10 2 9 4 5
(a) Write down the mode.
(b) Work out the median.
Answer/Explanation
Ans:
(a) 4
(b) 7 nfww
Question
Marco throws a six-sided dice 27 times.
The bar chart shows his results.
(a) Write down the mode.
(b) Work out the probability that Marco throws a number less than 5.
(c) Calculate the mean.
Answer/Explanation
Ans:
(a) 4 cao
(b) \(\frac{21}{27}\) oe isw
(c) 3.33(3…)
Question
Cheryl recorded the midday temperatures in Seoul for one week in January.
(a) Write down the mode.
Answer/Explanation
Ans: -3
(b) On how many days was the temperature lower than the mode?
Answer/Explanation
Ans: 4
Question
These are the heights, correct to the nearest centimetre, of 12 children.
132 114 151 130 132 145 163 142 153 170 132 125
Find the median height.
Answer/Explanation
Ans: 137