(a) Explain each of the following measures of central tendency
(i) mean;
(ii) median;
(iii) mode
(b) Calculate the mean, median and mode of the following set of numbers: 21, 22, 23,24, 25, 26, 23, 28, 29, 30, 24, 31, 34, 23
Explanation
(a) Means is the average of a series of figures or values. It is obtained by dividing the sum of these figures by the total number of the figures or values. It is also the average of a collection of observation.
(ii) The median is an average which is the middle value when figures are arranged in order of magnitude. In an even distribution the median is the average of the two middle numbers.
(iii) Mode is a measure of central tendency. It tells us the observation which is most popular, that is, the most frequently occurring value in a distribution. From the following observations 1, 3, 4, 3, 5, 3, mode is 3
(b) Mean = \(\frac{21 +22+23+23+23+24+24+25+26+27+28+29+30+31+34} {15}\)
= \(\frac{390} {15}\) =26
median: 21, 22, 23, 23, 23, 24, 24, 25 26, 27, 28, 29, 30, 31, 34, = 25
Mode = 23