| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2015 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate statistics from grouped frequency table |
| Difficulty | Moderate -0.8 This is a straightforward grouped data calculation requiring standard formulas for mean and standard deviation from a frequency table. It involves routine arithmetic with midpoints and the calculator-friendly formula, with no conceptual challenges or problem-solving—purely mechanical application of well-practiced techniques. |
| Spec | 2.02g Calculate mean and standard deviation |
| Time (seconds) | 1 -- 25 | 26 -- 35 | 36 -- 45 | 46 -- 55 | 56 -- 90 |
| Number of people | 4 | 24 | 38 | 34 | 20 |
| Answer | Marks |
|---|---|
| 2 | mid points 13, 30.5, 40.5, 50.5, 73 |
| Answer | Marks |
|---|---|
| sd = 14.9 | M1 |
| Answer | Marks |
|---|---|
| A1 5 | Attempt at midpoints at least 3 correct |
Question 2:
2 | mid points 13, 30.5, 40.5, 50.5, 73
Mean =
4×13 +24×30.5 +38×40.5 +34×50.5 +20×73
120
5500
= = 45.8
120
var =
2 2 2 2 2
4×13 +24×30.5 +38×40.5 +34×50.5 +20×73
120
2
– (45.8…)
278620
2
= – 45.8…
120
2
= 2321.8333 – 45.8…
sd = 14.9 | M1
M1
A1
M1
A1 5 | Attempt at midpoints at least 3 correct
Using their midpoints i.e. cw, ucb, 1/2 cw
and freqs into correct formula must be
divided by 120
Correct answer from correct working
Evaluating
2
∑ fx −their x 2 must see their 45.8 2
120
subtracted allow cw etc
Correct answer120 people were asked to read an article in a newspaper. The times taken, to the nearest second, by the people to read the article are summarised in the following table.
\begin{tabular}{|c|c|c|c|c|c|}
\hline
Time (seconds) & 1 -- 25 & 26 -- 35 & 36 -- 45 & 46 -- 55 & 56 -- 90 \\
\hline
Number of people & 4 & 24 & 38 & 34 & 20 \\
\hline
\end{tabular}
Calculate estimates of the mean and standard deviation of the reading times. [5]
\hfill \mbox{\textit{CAIE S1 2015 Q2 [5]}}