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

1FoundationSAQ-SMeasures of central tendency (mean, median, mode)s5 marksPaper 1~8 min
A group of 88 students recorded the number of books they read during a holiday. The results are: 2, 3, 5, 6, 8, 10, 132,\ 3,\ 5,\ 6,\ 8,\ 10,\ 13
(a)
State the range of the data. [1 mark]
(b)
Find the median number of books read. [2 marks]
(c)
Find the mean number of books read. [2 marks]
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Solutions

2FoundationSAQ-SMeasures of central tendency (mean, median, mode)s5 marksPaper 1~8 min
The heights (in cm) of 7 plants in a greenhouse are: 30,  15,  22,  12,  25,  18,  2030,\; 15,\; 22,\; 12,\; 25,\; 18,\; 20
(a)
State the median height. [1 mark]
(b)
A new plant of height 28 cm28\,\text{cm} is added to the group. Calculate the new median height. [2 marks]
(c)
The mean height of the original 7 plants is 1427 cm\frac{142}{7}\,\text{cm}. Determine whether the mean or the median changes by the greater amount when the new plant is added. [2 marks]
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Solutions

3MasterySAQ-SMeasures of central tendency (mean, median, mode)s5 marksPaper 1~8 min
The weights (in kg) of eight rugby players are: 73, 78, 81, 85, 90, 94, 97, x73,\ 78,\ 81,\ 85,\ 90,\ 94,\ 97,\ x The mean weight of the eight players is 84.875 kg84.875\,\text{kg}.
(a)
Show that x=81x = 81. [2 marks]
(b)
Hence find the median weight of the eight players. [3 marks] Correction note (self-verify): Clean integer mean requires clean sum. Let the seven given values be $73, 78, 81, 85, 90, 94, 97$ with sum =598= 598. Mean =598+x8= \frac{598+x}{8}. For x=82x=82: mean =85= 85. Adopt this clean version below. The weights (in kg) of eight rugby players are: 73, 78, 81, 85, 90, 94, 97, x73,\ 78,\ 81,\ 85,\ 90,\ 94,\ 97,\ x The mean weight of the eight players is 85 kg85\,\text{kg}. (a) Show that x=82x = 82. [2 marks] (b) Hence find the median weight of the eight players. [3 marks]
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Solutions

4ChallengeSAQ-LMeasures of spread (range, variance, standard deviation) s8 marksPaper 1~12 min

Data

xˉ=∑i=1nxin,s2=∑i=1n(xi−xˉ)2n−1,s=s2\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}, \qquad s^2 = \frac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n-1}, \qquad s = \sqrt{s^2}
A biologist studies the growth of a plant species under controlled conditions. She measures the heights (in cm) of a random sample of 10 plants after 4 weeks: 22,  25,  28,  30,  32,  33,  35,  38,  42,  4522, \; 25, \; 28, \; 30, \; 32, \; 33, \; 35, \; 38, \; 42, \; 45
(a)
Determine the range of the sample. [1 mark]
(b)
Determine the sample variance of the heights, giving your answer correct to three significant figures. [3 marks]
(c)
The biologist decides to express all heights in millimetres rather than centimetres. Determine the sample variance of the heights measured in millimetres. [2 marks]
(d)
Analyse how the sample standard deviation would change if an 11th plant, with height equal to the mean of the original 10 plants, were added to the sample. Justify your answer without performing a full recalculation. [2 marks]
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Solutions

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