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Descriptive Statistics · Paper 2 — Free Maths AA HL Practice Questions

1MasterySAQ-SMeasures of central tendency (mean, median, mode)s8 marksPaper 2~12 min
The heights (in cm) of 11 players in a basketball squad are listed in ascending order: 188, 191, 194, 196, 197, 198, 200, 202, 205, 207, x188,\ 191,\ 194,\ 196,\ 197,\ 198,\ 200,\ 202,\ 205,\ 207,\ x where x>207x > 207 is the height of the tallest player.
(a)
Given that the mean height of the 11 players is 198 cm198\,\text{cm}, calculate the value of xx. [3 marks]
(b)
Using your value of xx from part (a), calculate the interquartile range of the heights. [2 marks]
(c)
After the squad is selected, the player of height 194 cm194\,\text{cm} is injured and replaced by a new player of height 210 cm210\,\text{cm}. Determine whether the mean and the median each increase, decrease, or stay the same. Justify both answers. [3 marks]
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