| Date | November 2008 | Marks available | 2 | Reference code | 08N.1.sl.TZ0.6 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 6 | Adapted from | N/A |
Question
The distribution of the weights, correct to the nearest kilogram, of the members of a football club is shown in the following table.
On the grid below draw a histogram to show the above weight distribution.
Write down the mid-interval value for the \(40 - 49\) interval.
Find an estimate of the mean weight of the members of the club.
Write down an estimate of the standard deviation of their weights.
Markscheme
(A1)(A1) (C2)
Notes: (A1) for all correct heights, (A1) for all correct end points (\(39.5\), \(49.5\) etc.).
Histogram must be drawn with a ruler (straight edge) and endpoints must be clear.
Award (A1) only if both correct histogram and correct frequency polygon drawn.
[2 marks]
\(44.5\) (A1) (C1)
Note: If (b) is given as \(45\) then award
(b) \(45\) (A0)
(c) \(58.8{\text{ kg}}\) (M1)(A1)(ft) or (C2)(ft) if no working seen.
(d) \(8.44\) (C1)
[1 mark]
Unit penalty (UP) applies in this question.
\({\text{Mean}} = \frac{{44.5 \times 6 + 54.5 \times 18 + \ldots }}{{42}}\) (M1)
Note: (M1) for a sum of frequencies multiplied by midpoint values divided by \(42\).
\( = 58.3{\text{ kg}}\) (A1)(ft) (C2)
Note: Award (A1)(A0)(AP) for \(58\).
Note: If (b) is given as \(45\) then award
(b) \(45\) (A0)
(c) \(58.8{\text{ kg}}\) (M1)(A1)(ft) or (C2)(ft) if no working seen.
(d) \(8.44\) (C1)
[2 marks]
\({\text{Standard deviation}} = 8.44\) (A1) (C1)
Note: If (b) is given as \(45\) then award
(b) \(45\) (A0)
(c) \(58.8{\text{ kg}}\) (M1)(A1)(ft) or (C2)(ft) if no working seen.
(d) \(8.44\) (C1)
[1 mark]
Examiners report
The class boundaries needed to be correctly identified to permit full credit to be given. Weight being a continuous variable and given to the nearest kg meant that the lowest class boundary was \(39.5\). Thereafter, the use of midpoints is standard.
(a) The endpoints of the bars caused problems for all but a very few candidates. Diagrams drawn without a ruler were also penalized.
The class boundaries needed to be correctly identified to permit full credit to be given. Weight being a continuous variable and given to the nearest kg meant that the lowest class boundary was \(39.5\). Thereafter, the use of midpoints is standard.
(b) This was well attempted by the majority; it acted as a prompt for the following parts.
The class boundaries needed to be correctly identified to permit full credit to be given. Weight being a continuous variable and given to the nearest kg meant that the lowest class boundary was \(39.5\). Thereafter, the use of midpoints is standard.
(c) (d) resulted in many incorrect answers; it was expected that the GDC would be used for these parts of the question, though a number calculated the mean by hand.
The class boundaries needed to be correctly identified to permit full credit to be given. Weight being a continuous variable and given to the nearest kg meant that the lowest class boundary was \(39.5\). Thereafter, the use of midpoints is standard.
(c) (d) resulted in many incorrect answers; it was expected that the GDC would be used for these parts of the question, though a number calculated the mean by hand.
