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

Statistics: exam review Exam review Answers

Section A: short questions

    1. (a) Stratified sampling
    2. (b) 8
    3. (c) (i) discrete, (ii) continuous
    4. (d) \(34.5\le t<35.5\)
    1. (a) 9
    2. (b) 1
    3. (c) 1.95
    4. (d) 1.30
    5. (e) 13
    1. (a) \(x=8\)
    2. (b) mean \(=65.1\), standard deviation \(=4.5\)
    3. (c) median \(=64.4\), IQR \(=7.2\)
    1. (a) 14
    2. (b) 4.12
    3. (c) the second clinic is more consistent (smaller standard deviation)
    4. (d) 17 to 33
    1. (a) median \(=47\), \(Q_1=42\), \(Q_3=58\)
    2. (b) 16
    3. (c) upper fence \(=82\) and 87 is greater than this
    4. (d) mean 52 to 48.5, median 47 to 46; the median changes less, so it is the better measure
    1. (a) 25
    2. (b) Courier A: 11; Courier B: 7
    3. (c) Courier B is more consistent (smaller IQR); the median of Courier A is lower (25 compared with 26)
    4. (d) fences 11.5 and 39.5; 47 is an outlier
    1. (a) 60
    2. (b) 37.6
    3. (c) 32.3
    1. (a) 69
    2. (b) 69.7
    1. (a) 3
    2. (b) 13
    3. (c) 2

Section B: long questions

    1. (a) about 30
    2. (b) \(Q_1\approx20.9\), \(Q_3\approx38.3\), IQR \(\approx17.4\)
    3. (c) about 10
    4. (d) about 46.7
    5. (e) 0–10: 6, 10–20: 12, 20–30: 22, 30–40: 24, 40–50: 12, 50–60: 4
    6. (f) about 29.5
    1. (a) (5, 28.5)
    2. (b) −0.894
    3. (c) strong negative correlation
    4. (d) \(y=-0.925x+33.1\)
    5. (e) Each extra hour of training per week is linked to a fall of 0.925 minutes in the 5 km time; a runner who does no training has a predicted time of 33.1 minutes
    6. (f) 28.0
    7. (g) 19.2; unreliable, because 15 hours is outside the range of the data (extrapolation)
    8. (h) Correlation does not prove causation: other factors, such as fitness or age, may affect both
    1. (a) ranks of the ages: 1, 2, 3, 4, 5, 6, 7, 8; ranks of the numbers of words: 1, 2, 3.5, 3.5, 5, 6, 7, 8
    2. (b) 0.994
    3. (c) strong positive association: older toddlers tend to know more words
    4. (d) 0.873
    5. (e) The points follow a curve that rises ever more steeply; the order agrees almost perfectly, but the points are not on a straight line
    6. (f) \(r_s=0.996\), \(r=0.832\)
    7. (g) \(r_s\) changes by 0.00179 and \(r\) by 0.0410; \(r_s\) is hardly affected because the order is kept
    1. (a) 2
    2. (b) \(Q_1=1\), \(Q_3=4\), IQR \(=3\)
    3. (c) upper fence \(8.5\), and \(9>8.5\)
    4. (d) outliers 4 and 73; the whiskers end at 17 and 52
    1. (a) \(Q_1=24\), \(Q_3=35\); upper fence \(51.5\), and \(70>51.5\)
    2. (b) \(r=0.811\); \(0.811>0.632\), so there is significant evidence of positive correlation
    3. (c) \((21.4, 32.8)\); \(y=2x-10\)
    4. (d) \(32.8\); the line of \(y\) on \(x\) is for estimating \(y\) from \(x\) only

jmaths.xyz · AI SL · 13.3.10 Unit review