Further Mathematics Paper 2, May/June. 2014
 Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Main
Weakness/Remedies
Strength

Question 7

The table shows the distribution of the lengths of 20 iron rods measured in metres.

 Length (m) 1.0 -1.1 1.2  - 1.3 1.4 - 1.5 1.6  - 1.7 1.8 -1.9 Frequency 2 3 8 5 2

Using an assumed means of 1.45, calculate the mean of the distribution.

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Observation

This question was reportedly attempted by majority of the candidates and their      performancewas described as fair. However, it was observed that some candidates   calculated the mean without using the assumed mean. This was wrong as they were  expected to use the assumed mean. Some others were reported not to manipulate the  decimals involved correctly.
Candidates were expected to obtain the following table:

 Length f Class mid-point (x) d=x-a fd 1.0 -1.1 2 1.05 - 0.4 - 0.8 1.2 – 1.3 3 1.25 - 0.2 - 0.6 1.4 -1.5 8 1.45 0.0 0.0 1.6 -1.7 5 1.65 0.2 1.0 1.8 -1.9 2 1.85 0.4 0.8 ∑f = 20 ∑fd = 0.4

Using the table, the mean would be calculated using the formula,
mean = A+  , where A =  assumed mean = 1.45,  ∑fd = 0.4 and ∑f = 20. Therefore, mean = 1.45 +