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

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

A group of 10 students took a mathematics test. Their scores, out of 100, are recorded below:

52,\ 58,\ 63,\ 67,\ 71,\ 71,\ 78,\ 84,\ 96

(a)

State the mode of these scores. [1 mark]

(b)

Find the median of these scores. [2 marks]

(c)

Calculate the mean of these scores, giving your answer correct to one decimal place. [2 marks]

(d)

A student claims that the mean is the most appropriate measure of central tendency to represent this data set. Determine whether this claim is justified. [2 marks]

Solutions

2MasterySAQ-SMeasures of central tendency (mean, median, mode)5 marksPaper 1~8 min

A small business records the number of customer complaints received each day over a 10-day period. The data, in complaints per day, are:

3,\ 5,\ 7,\ 8,\ 8,\ 9,\ 11,\ 12

(a)

Show that the mean number of complaints per day is

7.6

. [2 marks]

(b)

The business manager removes the two extreme values (the smallest and the largest) to reduce the effect of outliers. Calculate the mean of the remaining eight values. [2 marks]

(c)

The manager claims that removing the extreme values gives a more reliable measure of the typical daily complaints. Determine whether the median of the original dataset supports or contradicts this claim, justifying your answer. [1 mark]

Solutions

3ChallengeSAQ-LMeasures of spread (range, variance, standard deviation)8 marksPaper 1~12 min

A factory produces cylindrical metal rods. The diameters (in mm) of a random sample of 8 rods are:

12.4,\ 12.7,\ 12.1,\ 12.9,\ 12.3,\ 12.6,\ 12.2,\ 12.8

(a)

Determine the range and the sample variance of the diameters. [4 marks]

(b)

A second sample of 6 rods from a different production line has diameters with a mean of

12.5\,\text{mm}

and a sample standard deviation of

0.35\,\text{mm}

. Determine the sample standard deviation of the combined sample of all 14 rods, and state whether it is larger or smaller than the standard deviation of the second sample alone. [4 marks]

Solutions

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