| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2019 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Find coded sums from raw data |
| Difficulty | Easy -1.2 This is a straightforward computational question requiring only direct substitution into coding formulas and application of the variance formula. It involves routine arithmetic with no conceptual challenges—students simply subtract 120 from each value, sum the results, square and sum for the second part, then apply the standard variance formula. This is easier than average A-level work as it's purely mechanical calculation with no problem-solving or interpretation required. |
| Spec | 2.02g Calculate mean and standard deviation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\Sigma(t-120) = -25+6-3+15+0+5-6-1+16 = 7\) | M1 | Attempt to sum both \((t-120)\) and \((t-120)^2\). Correct answer using \(\Sigma t - 9 \times 120\) and \(\Sigma(t-120)^2\) |
| \(\Sigma(t-120)^2 = 25^2+6^2+3^2+15^2+0^2+5^2+6^2+1^2+16^2 = 1213\) | A1 | Both correct, www. SC correct answer no working B1B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\text{Var} = \dfrac{\Sigma(t-120)^2}{9} - \left(\dfrac{\Sigma(t-120)}{9}\right)^2 = \dfrac{\textit{their } 1213}{9} - \left(\dfrac{\textit{their } 7}{9}\right)^2\) | M1 | Using two coded values in correct formula including finding \(\Sigma t\) from 7 etc |
| \(= 134(.2)\) | A1 | Correct answer. SC if correct variance obtained by another method from raw data give SCB1 |
## Question 1:
### Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\Sigma(t-120) = -25+6-3+15+0+5-6-1+16 = 7$ | **M1** | Attempt to sum both $(t-120)$ and $(t-120)^2$. Correct answer using $\Sigma t - 9 \times 120$ and $\Sigma(t-120)^2$ |
| $\Sigma(t-120)^2 = 25^2+6^2+3^2+15^2+0^2+5^2+6^2+1^2+16^2 = 1213$ | **A1** | Both correct, www. **SC** correct answer no working **B1B1** |
### Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\text{Var} = \dfrac{\Sigma(t-120)^2}{9} - \left(\dfrac{\Sigma(t-120)}{9}\right)^2 = \dfrac{\textit{their } 1213}{9} - \left(\dfrac{\textit{their } 7}{9}\right)^2$ | **M1** | Using two coded values in correct formula including finding $\Sigma t$ from 7 etc |
| $= 134(.2)$ | **A1** | Correct answer. **SC** if correct variance obtained by another method from raw data give **SCB1** |
---1 The times, $t$ seconds, taken to swim 100 m were recorded for a group of 9 swimmers and were found to be as follows.
$$\begin{array} { l l l l l l l l l }
95 & 126 & 117 & 135 & 120 & 125 & 114 & 119 & 136
\end{array}$$
(i) Find the values of $\Sigma ( t - 120 )$ and $\Sigma ( t - 120 ) ^ { 2 }$.\\
(ii) Using your values found in part (i), calculate the variance of $t$.\\
\hfill \mbox{\textit{CAIE S1 2019 Q1 [4]}}