CAIE S1 2023 March — Question 1 8 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2023
SessionMarch
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicData representation
TypeDraw cumulative frequency graph from frequency table (unequal class widths)
DifficultyModerate -0.8 This is a straightforward grouped data question requiring standard techniques: plotting cumulative frequency (routine), reading a percentile from the graph (direct lookup), and calculating an estimated mean using midpoints (standard formula application). All three parts are textbook exercises with no problem-solving or conceptual challenges.
Spec2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread
Each year the total number of hours, \(x\), of sunshine in Kintoo is recorded during the month of June. The results for the last 60 years are summarised in the table.
\(x\)\(30 \leqslant x < 60\)\(60 \leqslant x < 90\)\(90 \leqslant x < 110\)\(110 \leqslant x < 140\)\(140 \leqslant x < 180\)\(180 \leqslant x \leqslant 240\)
Number of years48142572
  1. Draw a cumulative frequency graph to illustrate the data. [3]
  2. Use your graph to estimate the 70th percentile of the data. [2]
  3. Calculate an estimate for the mean number of hours of sunshine in Kintoo during June over the last 60 years. [3]
Question 1:
AnswerMarks Guidance
1(a)Upper value 60 90 110 140 180 240
cf 4 12 26 51 58 60B1 All cumulative frequencies stated.
May be under data table, condone omission of 4.
May be read accurately from graph, must include 4.
AnswerMarks
M1At least 5 points plotted at class upper end points, daylight rule
tolerance.
Linear cf scale 0 ⩽ cf ⩽ 60, linear time scale 30 ⩽ time ⩽ 240
with at least 3 values identified on each axis.
AnswerMarks
A1All points plotted correctly. Curve drawn (within tolerance),
no ruled segments, and joined to (30,0).
Axes labelled ‘cumulative frequency’ and ‘hours [of
sunshine]’ (OE including appropriate title).
3
AnswerMarks Guidance
1(b)[60 × 0.7 = ] 42 M1
126A1 FT Must be clear evidence on graph of use of 42, e.g. an
appropriate mark on either axis, appropriate mark on curve.
FT from increasing cf graph only read at 42 only.
2
AnswerMarks Guidance
Upper value60 90
cf4 12
QuestionAnswer Marks
AnswerMarks Guidance
1(c)Midpoints: 45, 75, 100, 125, 160, 210 B1
in formula.
445+875+14100+25125+7160+2210
[Mean =]
60
 6845
=
 
AnswerMarks Guidance
 60 M1 Correct mean formula using their 6 midpoints (must be within
class, not upper bound, lower bound), condone 1 data error
If correct midpoints seen accept
180+600+1400+3125+1120+420
.
60
1
= 114, 114
AnswerMarks Guidance
12A1 Accept 114.1, 114.08[3…]
1
If A1 not awarded, SC B1 for 114, 114 , 114.1 or
12
114.08[3…].
3
AnswerMarks Guidance
QuestionAnswer Marks 
Question 1:
--- 1(a) ---
1(a) | Upper value 60 90 110 140 180 240
cf 4 12 26 51 58 60 | B1 | All cumulative frequencies stated.
May be under data table, condone omission of 4.
May be read accurately from graph, must include 4.
M1 | At least 5 points plotted at class upper end points, daylight rule
tolerance.
Linear cf scale 0 ⩽ cf ⩽ 60, linear time scale 30 ⩽ time ⩽ 240
with at least 3 values identified on each axis.
A1 | All points plotted correctly. Curve drawn (within tolerance),
no ruled segments, and joined to (30,0).
Axes labelled ‘cumulative frequency’ and ‘hours [of
sunshine]’ (OE including appropriate title).
3
--- 1(b) ---
1(b) | [60 × 0.7 = ] 42 | M1 | 42 may be implied by clear use on graph.
126 | A1 FT | Must be clear evidence on graph of use of 42, e.g. an
appropriate mark on either axis, appropriate mark on curve.
FT from increasing cf graph only read at 42 only.
2
Upper value | 60 | 90 | 110 | 140 | 180 | 240
cf | 4 | 12 | 26 | 51 | 58 | 60
Question | Answer | Marks | Guidance
--- 1(c) ---
1(c) | Midpoints: 45, 75, 100, 125, 160, 210 | B1 | At least 5 correct mid-points seen, check by data table or used
in formula.
445+875+14100+25125+7160+2210
[Mean =]
60
 6845
=
 
 60  | M1 | Correct mean formula using their 6 midpoints (must be within
class, not upper bound, lower bound), condone 1 data error
If correct midpoints seen accept
180+600+1400+3125+1120+420
.
60
1
= 114, 114
12 | A1 | Accept 114.1, 114.08[3…]
1
If A1 not awarded, SC B1 for 114, 114 , 114.1 or
12
114.08[3…].
3
Question | Answer | Marks | Guidance
Each year the total number of hours, $x$, of sunshine in Kintoo is recorded during the month of June. The results for the last 60 years are summarised in the table.

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
$x$ & $30 \leqslant x < 60$ & $60 \leqslant x < 90$ & $90 \leqslant x < 110$ & $110 \leqslant x < 140$ & $140 \leqslant x < 180$ & $180 \leqslant x \leqslant 240$ \\
\hline
Number of years & 4 & 8 & 14 & 25 & 7 & 2 \\
\hline
\end{tabular}

\begin{enumerate}[label=(\alph*)]
\item Draw a cumulative frequency graph to illustrate the data. [3]

\item Use your graph to estimate the 70th percentile of the data. [2]

\item Calculate an estimate for the mean number of hours of sunshine in Kintoo during June over the last 60 years. [3]
\end{enumerate}

\hfill \mbox{\textit{CAIE S1 2023 Q1 [8]}}
This paper (7 questions)
View full paper
Q1 8 Q2 7 Q3 6 Q4 3 Q5 3 Q6 11 Q7 12