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Descriptive Statistics · Paper 1 — Free Maths AI SL Practice Questions

What this topic covers

This is the topic examiners lean on hardest, because it's the one place they can test whether you actually understand what a number means, not just whether you can press the right calculator button. A GDC will hand you $r$ , a $p$ -value, or a confidence interval in seconds — the marks live in knowing which tool to reach for, reading the question for the tail direction, and finishing with a sentence back in context. Four threads run through it: describing data you already have, inferring about a population you don't, modelling chance for single events, and modelling chance across a whole range of outcomes. They constantly borrow from each other, so treat this as one connected chapter, not four separate ones.

Read the full Statistics and Probability lesson notes →

1FoundationSAQ-SMeasures of central tendency (mean, median, mode)5 marksPaper 1~8 min

A small company records the number of days each of its 8 employees was absent from work last month. The data set is:

2,\ 5,\ 3,\ 8,\ 2,\ 4,\ 5,\ 3

(a)

Calculate the mean number of days absent. [2 marks]

(b)

Find the median number of days absent. [2 marks]

(c)

The manager states: "The mean is the most appropriate measure of central tendency to represent this data." Justify whether you agree or disagree with this statement. [1 mark]

Solutions

2FoundationSAQ-SMeasures of central tendency (mean, median, mode)7 marksPaper 1~11 min

A gardener measures the heights (in cm) of 7 sunflower plants:

12,\ 15,\ 11,\ 18,\ 15,\ 14,\ 20

(a)

Find the mean height. [2 marks]

(b)

Find the median height. [2 marks]

(c)

A plant food company claims that sunflower plants grown with their product have a mean height of

18\,\text{cm}

. The gardener adds an eighth plant of height

h\,\text{cm}

, grown using the company's product, to the dataset. Determine the value of

h

such that the mean height of all eight plants equals

16\,\text{cm}

, and state whether this supports the company's claim. [3 marks]

Solutions

3MasterySAQ-SMeasures of central tendency (mean, median, mode)5 marksPaper 1~8 min

The ages (in years) of eight people in a cycling club are:

22,\ 25,\ 27,\ 30,\ 33,\ 35,\ 38,\ y

(a)

Show that if the mean age is

30

years, then

y = 30

. [2 marks]

(b)

Hence find the median age of the group. [1 mark]

(c)

Two new members join the club: one aged

30

and one aged

40

. Determine the mode of the ten ages and explain whether the mean age of the group increases, decreases, or stays the same. [2 marks]

Solutions

4ChallengeSAQ-LMeasures of central tendency (mean, median, mode)8 marksPaper 1~12 min

The following table shows the number of hours spent on social media per week by a group of

20

students. Hours —

0-4

—

5-9

—

10-14

—

15-19

—

20-24

Frequency —

3

—

7

—

6

—

3

—

1

(a)

Calculate an estimate for the mean number of hours spent on social media per week, using the midpoint of each interval. [3 marks]

(b)

Using a cumulative frequency table, determine the median class. State the modal class. [2 marks]

(c)

A new student joins the group and spends between

25

and

29

hours per week on social media. Calculate the new estimated mean and determine whether the modal class and median class change. Hence evaluate which measure of central tendency — the mean or the modal/median class — is more affected by this addition, justifying your answer. [3 marks]

Solutions

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