Theory question 112
Measures of Central Tendency(a) A study on average daily temperature in °C over a period of 12 months are: 24, 25, 23, 27, 26, 28, 29, 30, 27, 26, 25 and 24
(i) Find the: (I) mean (II) median (III) mode of the data
(ii) State, with explanation, which of the measures in 12(a)(i) best represents the data?
(b) Two towns lie on the same meridian and have latitudes of 15°N and 36°N. (i) Illustrate the information in a diagram (ii) Calculate, correct to three significant figures, the distance between the towns [Take π = 22/7 and R = 6400 km]
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(a)(i)(I) Mean = 314 ÷ 12 ≈ 26.17 °C
(II) Ordered: 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 29, 30; median = (26 + 26)/2 = 26 °C
(III) Modes: 24, 25, 26 and 27 (each appears twice)
(ii) The median (or the mean): the data has no extreme values, both are close to the centre; the mode is not useful because there are four modes
(b)(i) Sphere with the equator, one meridian and the two towns at 15°N and 36°N on it
(ii) Angle = 36° − 15° = 21°; distance = 21/360 × 2 × 22/7 × 6400 ≈ 2,350 km
Both towns are north, so subtract the latitudes.