The data below represents the mean score of students who did the commerce examination at five different schools.             School Number of students Mean score I P 88 II 40 70 III 50 62 IV 70 75 V 65 55           i.            If the average score of all the students is 69.2, find the number of students who sat the examination in school I.                                                    ii.            Using the mean scores, represent this data in a bar diagram    Mutuku is trying to convince his classmate Muriuki that that there are four scales of measurement in statistics. Muriuki is of a contrary opinion. By discussing the scales of measurement, justify who among the two is correct in his argument.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...