Numeracy Intermediate November 2020 Unit 1 Q10
10. There are 600 pupils in a school.
8 of these pupils are to be selected to discuss changes to the school uniform.
The headteacher has a spreadsheet of the names of all 600 pupils.
There are 600 rows of pupil names in the spreadsheet, starting at row 1.
There is one pupil name on each row.
The headteacher uses a systematic sampling method.
(a) The first pupil selected on the headteacher’s list is a boy whose name is in the 25th row.
Give the row numbers in the spreadsheet of the other 7 pupils who would be selected.
Complete the table below. [2]
| Pupil | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th |
|---|---|---|---|---|---|---|---|---|
| Row in the spreadsheet | 25th | ……… | ……… | ……… | ……… | ……… | ……… | ……… |
(b) Explain how the headteacher selected the first pupil. [1]
| Scheme | Marks | Comments | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| (600 ÷ 8 =) 75 | B1 | May be seen amongst other inappropriate working, but not from 75 written in the table | ||||||||||||||||
| B1 | FT ‘their 600 ÷ 8’ incorrectly evaluated |
| Scheme | Marks | Comments |
|---|---|---|
| States it is a random selection (from the first 75 pupils) | E1 | Ignore any additional spurious statements Allow for statement that implies ‘random’ selection, e.g. ‘sticks a pin in (a printout of) the spreadsheet’, ‘the headteacher picked a random number’, ‘everyone had a fair chance of selection’ Do not accept, e.g. ‘selects a random odd number’ ‘using a systematic sampling method’ without further clarification, |