The table shows the frequency distribution of heights (in cm) of pupils in a certain school.
(a) (i) Construct a cumulative frequency table. (ii) Use the table to draw a cumulative frequency curve.
(b) Using the curve, estimate the: (i)median height; (ii) inter quartile range (iii) percentage of students whose heights are most 130cm.
| Heights | 100-109 | 110-119 | 120-129 | 130-139 | 140-149 | 150-159 | 160-169 |
| Frequency | 27 | 58 | 130 | 105 | 50 | 25 | 5 |
(a) (i) Construct a cumulative frequency table. (ii) Use the table to draw a cumulative frequency curve.
(b) Using the curve, estimate the: (i)median height; (ii) inter quartile range (iii) percentage of students whose heights are most 130cm.
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Correct Answer: Option
Explanation:
(ii)
bi) Median 1/2 of N = 1/2 x 400 = 200
Cumulative frequency level From the curve, it is 118.5cm
(ii) Inter quartile range = upper quartile - lower quartile upper quartile
= 3/4 of N
= 3/4 x 400 = 300
Cumulative frequency level From the curve, it is 126.5cm
lower quartile = 1/4 of N
= 1/4 x 400 = 100
Cumulative frequency level From the curve, it is 111.0cm
Inter quartile range = 126.5cm -111.0cm = 15.5cm
(ii) From the curve, students whose heights are at most 130cm are 240.
Percentage óf students whose heights are at most 130cm = \(\frac{240}{400}\) x 100
= 60%
| Height (in cm) | Frequency |
| Not exceeding 99.5 | 0 |
| Not exceeding 109.5 | 27 |
| Not exceeding 119.5 | 85 |
| Not exceeding 129.5 | 215 |
| Not exceeding 139.5 | 320 |
| Not exceeding 149.5 | 370 |
| Not exceeding 159.5 | 395 |
| Not exceeding 169.5 | 400 |
(ii)
bi) Median 1/2 of N = 1/2 x 400 = 200
Cumulative frequency level From the curve, it is 118.5cm
(ii) Inter quartile range = upper quartile - lower quartile upper quartile
= 3/4 of N
= 3/4 x 400 = 300
Cumulative frequency level From the curve, it is 126.5cm
lower quartile = 1/4 of N
= 1/4 x 400 = 100
Cumulative frequency level From the curve, it is 111.0cm
Inter quartile range = 126.5cm -111.0cm = 15.5cm
(ii) From the curve, students whose heights are at most 130cm are 240.
Percentage óf students whose heights are at most 130cm = \(\frac{240}{400}\) x 100
= 60%