The following data shows marks obtained by students in a mathematics test; 6,9,5,0,5,3,7,5,2,7,10,2,9,8,0,6,2, 6,6,3,6,9,7,7,4,1,6,68 a. construct a frequency distribution table data using a discrete values 0, 1, 2, 10 b. State the modal score of the distribution c. if a student is chosen at random, what is the probability that a student scored more than 5 means d. Using assumed mean of 6, calculate the arithmetic mean score of the distribution

Data

6,9,5,0,5,3,7,5,2,7,10,2,9,8,0,6,2,6,6,3,6,9,7,7,4,1,6,8

(a) shown in the attachment

(b) 0.54

(c) 5.32

(a) The frequency distribution table has been added to this response.

The table contains four columns:

First column (x): The discrete values of the marks

Second column (f): The corresponding frequency of the marks

Third column (d) : The difference between each mark(x) and the assumed mean(A). i.e d = x - A (Where A = 6 from the question)

Fourth column (fd): The product of the first column and the third column. i.e f * d

(b) From the table, it can be deduced that the modal score is 6

This is because the score 6 has the highest number of frequency which is 6

(c) If a student is selected at random, the probability P(>5), that the student scored more than 5 is given as follows;

P( >5 ) = [The sum of frequencies of marks greater than 5] / [Total frequency]

P( >5 ) = [6 + 4 + 2 + 3 + 1] / [28]

P( >5 ) = 15 / 28 = 0.54

Therefore, the probability that the student scored more than 5 is 0.54

(d) To get the arithmetic mean, M, from the assumed mean A = 6, we use the following relation;

M = A + [∑fd / N]           -----------(*)

Where

N = total frequency = 28

A = 6

∑fd = sum of the items on the fourth column = -19

Substitute these values into equation (*)

M = 6 + [-19 / 28]

M = 149 / 28

M = 5.32

Therefore, the arithmetic mean is 5.32

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