2025 YCKSS PRELIMS P2 Q7

2025 YCKSS PRELIMS P2 Q7

Secondary 4
10 marks
  1. The grouped blood pressures of 50 patients are shown.
    1. Find the interval containing the median.[1]
    2. Calculate an estimate of the mean.[1]
    3. Calculate an estimate of the standard deviation.[1]
    4. A second group has standard deviation 22.1 mmHg. Comment on one difference between the distributions.[1]
    Blood pressure (mmHg)\(100<p\leq120\)\(120<p\leq140\)\(140<p\leq160\)\(160<p\leq180\)
    Frequency\(27\)\(12\)\(6\)\(5\)
  2. The back-to-back stem-and-leaf diagram shows heights in centimetres.
    1. Group B has interquartile range 10 cm. Show that \(x=3\).[3]
    2. A Group A student is selected at random. Find the probability their height is between 152 cm and 164 cm.[1]
    3. One student from each group is selected. Find the probability that one is above 160 cm and the other below 155 cm.[2]
    Group AStemGroup B
    \(1\)\(14\)\(2\)
    \(9\quad 8\quad 8\quad 2\)\(15\)3 \(x\) 7 8
    \(4\quad 3\quad 3\)\(16\)\(0\quad 2\quad 4\)
    \(3\quad 0\)\(17\)\(8\)
    Key: 1 | 14 | 2 means 141 cm in Group A and 142 cm in Group B.

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Answer:(a)(i) \(100<p\leq120\) (ii) \(125.6\text{ mmHg}\) (iii) \(20.1\text{ mmHg}\) (iv) second group less consistent (b)(i) \(x=3\) (ii) \(\frac12\) (iii) \(\frac7{30}\)

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