| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2016 |
| Session | March |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate mean from coded sums |
| Difficulty | Easy -1.8 This is a straightforward application of basic mean and coding formulas requiring only algebraic manipulation of two standard definitions. Students need only recall that mean = Σx/n and expand Σ(x-a) = Σx - na, making this significantly easier than average A-level questions which typically require multi-step problem-solving. |
| Spec | 2.02f Measures of average and spread |
| Answer | Marks | Guidance |
|---|---|---|
| \(\Sigma x = 862\) | B1 (1) | Must be stated or replaced in (ii); can see (i) and (ii) in any order |
| Answer | Marks | Guidance |
|---|---|---|
| \(362/10 + a = 86.2\); \(a = 50\) | M1, A1 (2) | \(86.2 \pm 36.2\) seen; correct answer, nfww |
## Question 1:
**(i)**
$\Sigma x = 862$ | B1 (1) | Must be stated or replaced in (ii); can see (i) and (ii) in any order
**(ii)**
$362/10 + a = 86.2$; $a = 50$ | M1, A1 (2) | $86.2 \pm 36.2$ seen; correct answer, nfww
---1 For 10 values of $x$ the mean is 86.2 and $\Sigma ( x - a ) = 362$. Find the value of\\
(i) $\Sigma x$,\\
(ii) the constant $a$.
\hfill \mbox{\textit{CAIE S1 2016 Q1 [3]}}