Theory question 106
StatisticsThe table shows the heights in cm of some seedlings in a certain garden:
Height (cm): 36 − 40, 41 − 45, 46 − 50, 51 − 55, 56 − 60
Frequency: 3, 9, 21, 12, 5
(a) Draw a cumulative frequency curve for the distribution (b) Using the curve in 6(a), find the semi-interquartile range.
Show the model answer
Model answer
(a) Upper boundaries 40.5, 45.5, 50.5, 55.5, 60.5; cumulative frequencies 3, 12, 33, 45, 50. Plot (start at (35.5, 0)) and join with a smooth curve.
(b) Q₁ (12.5th) ≈ 45.6 cm; Q₃ (37.5th) ≈ 52.4 cm.
Semi-interquartile range = ½(52.4 − 45.6) ≈ 3.4 cm (values read from a graph may differ slightly).
Explanation
Read the quartiles at a quarter and three quarters of the total frequency.