# WAEC standard on answering Statistics and Substitution

2018 May/June WAEC many students didn’t answer the question based on WAEC standard of answering questions so they didn’t get the full marks for it

The steps for answering statistics and Substitution in WAEC are outlined below:

Question 1: If the mean of m, n, s, p and q is 12, calculate the mean of (m + 4), (n – 3), (s + 6), (p – 2) and (q + 8). (WAEC, 2018)

According to the chief examiner for 2018 WAEC (Mathematics) the students were no so familiar with the question so it was not well attempted  so students didn’t get the full mark allocated to it below is WAEC standard for  answering such questions.

Question 2:

 Marks 1 2 3 4 5 Number of students m + 2 m – 1 2m – 3 m + 5 3m – 4

The table shows the distribution of marks scored by some students in a test.

1. If the mean mark is 3⁶/₂₃, find the value of m.
2. Find the: (i) inter-quartile range;
(ii) probability of selecting a student who scored at least 4 marks in the test. (WAEC, 2017).

The Chief Examiner reported that majority of the Candidates’ answered this question correctly but few had problems with the notation at least as they assumed it to be at most.
In part (a), the candidates’ did as expected by completing the fx column and summing as appropriate. They were expected to obtain the following table:

 x 1 2 3 4 5 Total f m+2 m-1 2m-3 m+5 3m-4 8m-1 fx m+2 2m-2 6m-9 4m+20 15m-20 28m-9

From the table, ∑fx=28m -9 and ∑fx= 8m – 1 ,
so that 28m – 9 / 8m – 1 = 75/ 23  and solving yields m = 3.

In part (b) (i), since m has been gotten to be 3, the table then becomes:

 x 1 2 3 4 5 f 5 2 3 8 5 Cf 5 7 10 18 23

88Therefore, interquartile range = 4 – 2 = 2.
Finally, in part (b) (ii), the probability of selecting a student who scored at least 4 marks is ¹³/₂₃   whereas most Candidates’ made use of at most 4 marks to obtain ¹⁸/₂₃  . Mathematics teachers are therefore advised to drill the students on the concept of probability as well as how do distinguish between “at least” and “at most”.In a community of 500 people, the 75th percentile age is 65 years while the 25th percentile age is 15 years. How many of the people are between 15 and 65 years? (WAEC, 2018).

2018 WAEC Past Question