Theory question 107
StatisticsA tyre manufacturing company researched into the life span of one type of their moto-cycle tyres. The results were as follows:
Distance (100km): 10 − 19, 20 − 29, 30 − 39, 40 − 49, 50 − 59, 60 − 69
Number of tyres: 30, 69, 93, 57, 36, 15
(a) Draw a histogram for the distribution.
(b) Use the histogram to estimate the mode.
Show the model answer
(a) Class boundaries 9.5, 19.5, 29.5, 39.5, 49.5, 59.5, 69.5 on the horizontal axis; bars of equal width 10 and heights 30, 69, 93, 57, 36, 15
(b) Modal class 29.5 − 39.5 (tallest bar); join the corners of the tallest bar to the adjacent bars and read where the lines cross
Mode ≈ 29.5 + (93 − 69)/[(93 − 69) + (93 − 57)] × 10 = 29.5 + 4 = 33.5, i.e. about 3350 km
Use class boundaries so the bars touch; the mode is read from the crossing lines on the tallest bar.