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IB Mathematics: Applications and Interpretation HL · 13.3: Statistics · 13.3.10

Statistics: exam review Exam review: second paper Answers

Section A: short questions

    1. (a) Stratified sampling
    2. (b) 10
    3. (c) (i) discrete, (ii) continuous
    4. (d) \(47.5\le t<48.5\)
    1. (a) 15
    2. (b) 2
    3. (c) 2.88
    4. (d) 1.31
    5. (e) 15
    1. (a) \(x=9\)
    2. (b) mean \(=754\), standard deviation \(=46.2\)
    3. (c) median \(=732\), IQR \(=60.5\)
    1. (a) 15
    2. (b) 2.38
    3. (c) the second player is more consistent (smaller standard deviation)
    4. (d) 14 to 26
    1. (a) median \(=25\), \(Q_1=22\), \(Q_3=28\)
    2. (b) 6
    3. (c) upper fence \(=37\) and 55 is greater than this
    4. (d) mean 27.3 to 24.5, median 25 to 24.5; the median changes less, so it is the better measure
    1. (a) 13
    2. (b) Route P: 10; Route Q: 7
    3. (c) Route Q is more consistent (smaller IQR); the median of Route P is higher (13 compared with 9)
    4. (d) fences −3.5 and 24.5; 21 is not an outlier
    1. (a) 58
    2. (b) 42.5
    3. (c) 18.2
    1. (a) 48.7
    2. (b) 49.3
    1. (a) 7
    2. (b) 10
    3. (c) 4

Section B: long questions

    1. (a) about 56
    2. (b) \(Q_1\approx38.9\), \(Q_3\approx73.6\), IQR \(\approx34.7\)
    3. (c) about 30
    4. (d) about 90
    5. (e) 0–20: 8, 20–40: 18, 40–60: 30, 60–80: 28, 80–100: 12, 100–120: 4
    6. (f) about 56
    1. (a) (8.5, 20.8)
    2. (b) 0.893
    3. (c) strong positive correlation
    4. (d) \(y=1.03x+12.0\)
    5. (e) Each extra 100 euros of advertising is linked to a rise of 1.03 thousand euros in sales; with no advertising the predicted sales are 12.0 thousand euros
    6. (f) 22.4
    7. (g) 37.9; unreliable, because 25 hundred euros is outside the range of the data (extrapolation)
    8. (h) Correlation does not prove causation: other factors, such as the season or special offers, may affect both
    1. (a) ranks of the hours of practice: 1, 2, 3, 4, 5, 6, 7, 8; ranks of the scores: 1, 2.5, 2.5, 4, 5.5, 5.5, 7, 8
    2. (b) 0.988
    3. (c) strong positive association: students who practise more tend to score higher
    4. (d) 0.947
    5. (e) The points follow a curve that rises quickly and then levels off; the order agrees almost perfectly, but the points are not on a straight line
    6. (f) \(r_s=0.992\), \(r=0.962\)
    7. (g) \(r_s\) changes by 0.00361 and \(r\) by 0.0148; \(r_s\) is hardly affected because the order is kept
    1. (a) 3
    2. (b) \(Q_1=2\), \(Q_3=4\), IQR \(=2\)
    3. (c) upper fence \(7\), and \(8>7\)
    4. (d) outliers 5 and 68; the whiskers end at 21 and 55
    1. (a) \(Q_1=15\), \(Q_3=24\); upper fence \(37.5\), and \(52>37.5\)
    2. (b) \(r=0.844\); \(0.844>0.632\), so there is significant evidence of positive correlation
    3. (c) \((6.6, 22.2)\); \(y=3x+2.4\)
    4. (d) \(22.2\); the line of \(y\) on \(x\) is for estimating \(y\) from \(x\) only

jmaths.xyz · AI HL · 13.3.10 Unit review