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Exam-Style Questions on AveragesProblems on Averages adapted from questions set in previous Mathematics exams. |
1. | GCSE Higher |
There is a total of 60 students in the school orchestra.
The mean age of the 24 boys is 15.5 years.
The mean age of the 36 girls is 16.4 years.
Calculate the mean age of all 60 students.
2. | GCSE Higher |
The following table shows the time taken by fifty people to answer their emails one day.
| Time, t minutes | Number of people |
| 0 < t ≤ 10 | 5 |
| 10 < t ≤ 20 | 12 |
| 20 < t ≤ 30 | 13 |
| 30 < t ≤ 40 | 15 |
| 40 < t ≤ 50 | 5 |
(a) In which class interval is the median?
(b) How many people took more than 20 minutes?
(c) What is the modal class interval?
(d) Find an estimate for the mean time taken showing all of your working.
3. | GCSE Higher |
A basket contains apples and oranges. The mean weight of the 9 apples in the basket is 265g. The mean weight of all 21 items of fruit in the basket is 290g.
Work out the mean weight of the oranges.
4. | GCSE Higher |
The following table show data collected by a researcher about the length of monitor lizards living in a park in Bangkok.
| Length (cm) | Frequency |
|---|---|
| \(0\lt l \le 50\) | 9 |
| \(50\lt l \le 100\) | 13 |
| \(100\lt l \le 150\) | 22 |
| \(150\lt l \le 200\) | 19 |
| \(200\lt l \le 250\) | 11 |
| \(250\lt l \le 300\) | 3 |
(a) Which is the modal group?
(b) Calculate an estimate for the mean lizard length.
(c) The researcher claims that the range of lengths must lie between 2m and 3m. Explain how the researcher came to this conclusion.
5. | IB Analysis and Approaches |
Jayne rolls a six-sided die 25 times.
The scores obtained are shown in the following frequency table.
$$ \begin{array}{|c|c|} \hline \text{Score} & \text{Frequency} \\ \hline 1 & 3 \\ 2 & 2 \\ 3 & 4 \\ 4 & 0 \\ 5 & p \\ 6 & q \\ \hline \end{array} $$It is given that the mean score is 4.
(a) Find the value of \( p \) and the value of \( q \).
Each of Jayne's scores is multiplied by 5 in order to determine the final score for a game she is playing.
(b) Write down the mean final score.
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