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
Answer:
(a) shown in the attachment
(b) 0.54
(c) 5.32
Explanation:
(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