(a)

\begin{align*} \boxed{1 \phantom{0} 5 \phantom{0} 8} \phantom{.} & 9 \phantom{.} \boxed{11 \phantom{0} 14 \phantom{0} 20} \\ \\ \text{Lower quartile} & = 5 \\ \\ \text{Median} & = 9 \\ \\ \text{Upper quartile} & = 14 \end{align*}

(b)

\begin{align*} \boxed{ 43 \phantom{0} 45 \phantom{0} 45 \phantom{0} 51 } & \boxed{ 54 \phantom{0} 57 \phantom{0} 58 \phantom{0} 60} \\ \\ \text{Lower quartile} & = {45 + 45 \over 2} \\ & = 45 \\ \\ \text{Median} & = {51 + 54 \over 2} \\ & = 52.5 \\ \\ \text{Upper quartile} & = {57 + 58 \over 2} \\ & = 57.5 \end{align*}

(c)

\begin{align*} \boxed{2 \phantom{0} 3 \phantom{0} 3 \phantom{0} 6 \phantom{0} 8 \phantom{0} 11} & \phantom{.} \boxed{12 \phantom{0} 15 \phantom{0} 15 \phantom{0} 17 \phantom{0} 21 \phantom{0} 22} \\ \\ \text{Lower quartile} & = {3 + 6 \over 2} \\ & = 4.5 \\ \\ \text{Median} & = {11 + 12 \over 2} \\ & = 11.5 \\ \\ \text{Upper quartile} & = {15 + 17 \over 2} \\ & = 16 \end{align*}

(d)

\begin{align*} \boxed{66 \phantom{0} 77 \phantom{0} 79 \phantom{0} 82} \phantom{.} & 87 \phantom{.} \boxed{87 \phantom{0} 93 \phantom{0} 96 \phantom{0} 98} \\ \\ \text{Lower quartile} & = {77 + 79 \over 2} \\ & = 78 \\ \\ \text{Median} & = 87 \\ \\ \text{Upper quartile} & = {93 + 96 \over 2} \\ & = 94.5 \end{align*}

(i)

\begin{align*} \text{Lower quartile} & = 19 \\ \\ \text{Median} & = 21 \\ \\ \text{Upper quartile} & = 25 \end{align*}

(ii)

\begin{align*} \text{Range} & = \text{Maximum} - \text{Minimum} \\ & = 27 - 16 \\ & = 11 \end{align*}

(i)

\begin{align*} \text{Median blood pressure level} & = 169 \end{align*}

(ii)

\begin{align*} \text{Interquartile range} & = \text{Upper quartile} - \text{Lower quartile} \\ & = 185 - 162 \\ & = 23 \end{align*}

(i)

\begin{align*} \text{Lower quartile} & = 0.05 \\ \\ \text{Median} & = 0.07 \\ \\ \text{Upper quartile} & = 0.086 \end{align*}

(ii)

\begin{align*} \text{Spread for lowest 25%} & = 0.05 - 0.02 \\ & = 0.03 \\ \\ \text{Spread for highest 25%} & = 0.13 - 0.086 \\ & = 0.044 \\ \\ \therefore \text{Lowest 25% is less spread out} & \text{ compared to the highest 25%} \end{align*}

(i)

\begin{align*} \boxed{168 \phantom{0} 180 \phantom{0} 185 \phantom{0} 192 \phantom{0} 192 \phantom{0} 195} & \boxed{195 \phantom{0} 196 \phantom{0} 198 \phantom{0} 200 \phantom{0} 205 \phantom{0} 213} \\ \\ a & = 168 \\ \\ b & = {185 + 192 \over 2} \\ & = 188.5 \\ \\ c & = {195 + 195 \over 2} \\ & = 195 \\ \\ d & = {198 + 200 \over 2} \\ & = 199 \\ \\ e & = 213 \end{align*}

(ii)

\begin{align*} d - b & = 199 - 188.5 \\ & = 10.5 \\ \\ d - b \text{ represents} & \text{ the interquartile range} \end{align*}

(iii)

\begin{align*} e - a & = 213 - 168 \\ & = 45 \\ \\ e - a \text{ represents} & \text{ the range} \end{align*}

(a)(i)

$$ \text{Type A} $$

(a)(ii)

$$ \text{Type C} $$

(b)

$$ \text{Type B (since the lower quartile, median and upper quartile is at the centre)} $$

(c)

$$ \text{Type B} $$

(a)(i)

\begin{align*} \text{Range} & = \text{Maximum} - \text{Minimum} \\ & = 82 - 48 \\ & = 34 \end{align*}

(a)(ii)

\begin{align*} \text{Median} & = 63 \end{align*}

(a)(iii)

\begin{align*} \text{Interquartile range} & = \text{Upper quartile} - \text{Lower quartile} \\ & = 67 - 59 \\ & = 8 \end{align*}

(b)(i)

\begin{align*} \text{Range} & = 86 - 45 \\ & = 41 \end{align*}

(b)(ii)

\begin{align*} \text{Median} & = 68 \end{align*}

(b)(iii)

\begin{align*} \text{Interquartile range} & = 78 - 64 \\ & = 14 \end{align*}

(c)

\begin{align} & \text{Agree. The median mass of students from school A (63 kg) is lower} \\ & \text{than the median mass of students from school B (68 kg).} \end{align}

(a)(i)

\begin{align*} \text{Range} & = \text{Maximum} - \text{Minimum} \\ & = 88 - 24 \\ & = 64 \end{align*}

(a)(ii)

\begin{align*} \text{Median} & = 56 \end{align*}

(a)(iii)

\begin{align*} \text{Interquartile range} & = \text{Upper quartile} - \text{Lower quartile} \\ & = 66 - 40 \\ & = 26 \end{align*}

(b)(i)

\begin{align*} \text{Range} & = 94 - 10 \\ & = 84 \end{align*}

(b)(ii)

\begin{align*} \text{Median} & = 42 \end{align*}

(b)(iii)

\begin{align*} \text{Interquartile range} & = 66 - 30 \\ & = 36 \end{align*}

(c)

\begin{align} & \text{Agree.} \\ & \text{The median score for the Geography examination (56 marks) is higher than the median score for the History examination (42 marks).} \\ & \text{The lowest score and the lower quartile score for the Geography examination is higher than that of the History examination as well.} \end{align}

(d)

\begin{align} & \text{The History examination has a wider spread of marks as the interquartile range (36 marks)} \\ & \text{is higher than the interquartile range of the Geography examination.} \end{align}

(a)(i)

\begin{align*} \text{Median} & = 15 \end{align*}

(a)(ii)

\begin{align*} \text{Interquartile range} & = \text{Upper quartile} - \text{Lower quartile} \\ & = 19 - 12 \\ & = 7 \end{align*}

(a)(iii)

\begin{align*} \text{No. of adults who spent less than or equals to 25 hours} & = 58 \\ \\ \text{No. of adults who spent more than 25 hours} & = 64 - 58 \\ & = 6 \end{align*}

(b)(i)

\begin{align*} \text{Median} & = 34 \end{align*}

(b)(ii)

\begin{align*} \text{Interquartile range} & = 52 - 28 \\ & = 24 \end{align*}

(c)

\begin{align} & \text{I agree.} \\ & \text{The median hours (34) teenagers spent watching TV is more than the median hours (15) adults spent watching TV.} \end{align}

(d)

\begin{align} & \text{The hours teenagers spent watching TV is more widely spread out as the interquartile range (24)} \\ & \text{is larger than the interquartile range (7) of the hours adults spent watching TV.} \end{align}

(a)(i)

\begin{align*} \text{Median} & = 40.5 \end{align*}

(a)(ii)

\begin{align*} \text{Interquartile range} & = \text{Upper quartile} - \text{Lower quartile} \\ & = 42.5 - 37.5 \\ & = 5 \end{align*}

(b)(i)

\begin{align*} \text{Median} & = 50 \end{align*}

(b)(ii)

\begin{align*} \text{Interquartile range} & = 53.5 - 44 \\ & = 9.5 \end{align*}

(c)

\begin{align} & \text{The lowest 25% is more spread out than the top 25%.} \end{align}

(d)

\begin{align} & \text{Luxury Country Club as the interquartile range (9.5) is larger than the interquartile range of Prestige Country Club (5).} \end{align}

(e)

\begin{align} & \text{For Prestige Country Club, members are mainly between 37.5 and 42.5 years old.} \\ & \text{The oldest member is 48.5 years old and the youngest member is 35 years old.} \\ \\ & \text{For Luxury Country Club, members are mainly between 44 and 53.5 years old.} \\ & \text{The oldest member is 60 years old and the youngest member is 30 years old.} \end{align}

(a)(i)

\begin{align*} \text{Median (for } X) & = 30 \\ \\ \text{Median (for } Y) & = 21 \end{align*}

(a)(ii)

\begin{align*} \text{Range (for } X) & = \text{Maximum} - \text{Minimum} \\ & = 50 - 10 \\ & = 40 \\ \\ \text{Range (for } Y) & = 37 - 12 \\ & = 25 \end{align*}

(a)(iii)

\begin{align*} \text{Interquartile range (for } X) & = \text{Upper quartile} - \text{Lower quartile} \\ & = 40 - 20 \\ & = 20 \\ \\ \text{Interquartile range (for } Y) & = 24 - 17 \\ & = 7 \end{align*}

(b)

\begin{align} & \text{Set X since the difference between the upper quartile and median is the same as} \\ & \text{the difference between the lower quartile and median.} \end{align}

(c)

\begin{align} & \text{Set X since the interquartile range (20) is higher.} \end{align}

(d)

$$ \text{Set Y}$$

(e)

$$ \text{Curve B} $$

(f)

\begin{align} & \text{Curve A to histogram P. The majority of the data is clustered around the median.} \\ \\ & \text{Curve B to histogram R. The cumulative frequency curve is a straight line.} \\ \\ & \text{Curve C to histogram Q. The majority of the data is clustered around the upper quartile.} \end{align}

(g)

\begin{align} & \text{Histogram P - Scores obtained for O Levels E maths paper} \\ \\ & \text{Histogram Q - Singapore’s aging population} \\ \\ & \text{Histogram R - Shoes of different sizes manufactured in a factory} \end{align}

\begin{align} & \text{Set X to histogram B. The bottom 25% of the data have a wide spread.} \\ \\ & \text{Set Y to histogram A. The data is evenly spread out.} \\ \\ & \text{Set Z to histogram C. The majority of the data is between the lower quartile and the upper quartile.} \end{align}