Question

answers must be written within the answer boxes provided. full marks are not necessarily awarded for a correct answer with no working. answers must be supported by working and/or explanations. solutions found from a graphic display calculator should be supported by suitable working. for example, if graphs are used to find a solution, you should sketch these as part of your answer. where an answer is incorrect, some marks may be given for a correct method, provided this is shown by written working. you are therefore advised to show all working.

1. maximum mark: 6

the following table shows the number of errors per page in a 100 page document.

number of errors	0	1	2	3	4

(a) state whether the data is discrete, continuous or neither. 1
(b) find the mean number of errors per page 2
(c) find the median number of errors per page 2
(d) write down the mode 1

Explanation:

Step1: Classify data type

Discrete data takes distinct, countable values. The number of errors per page is countable (0,1,2,3,4), so it is discrete.

Step2: Calculate total errors

Multiply each error count by page count, sum results.
$\text{Total errors} = (0 \times 28) + (1 \times 24) + (2 \times 20) + (3 \times 17) + (4 \times 11) = 0 + 24 + 40 + 51 + 44 = 159$

Step3: Calculate mean errors per page

Divide total errors by total pages (100).
$\text{Mean} = \frac{159}{100} = 1.59$

Step4: Locate median position

Median is the value at the $\frac{n+1}{2}$th position for $n=100$: $\frac{100+1}{2}=50.5$th value, average of 50th and 51st values.
Cumulative pages: 28 (0 errors), 28+24=52 (1 error). Both 50th and 51st values fall in the 1 error group, so median = 1.

Step5: Identify mode

Mode is the error count with the most pages. 0 errors has 28 pages, the highest frequency.

Answer:

(a) Discrete
(b) 1.59
(c) 1
(d) 0