CAIE S2 2016 November — Question 1 3 marks

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2016
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMeasures of Location and Spread
TypeStandard unbiased estimates calculation
DifficultyEasy -1.3 This is a straightforward application of standard formulas for unbiased estimates of mean and variance. Students need only recall that the sample mean estimates the population mean, and use the (n-1) divisor for unbiased variance. It requires basic arithmetic with a calculator and no problem-solving or conceptual insight beyond direct formula application.
Spec5.05b Unbiased estimates: of population mean and variance
1 The weights, in kilograms, of a random sample of eight 16-year old males are given below. $$\begin{array} { l l l l l l l l } 58.9 & 63.5 & 62.7 & 59.4 & 66.9 & 68.0 & 60.4 & 68.2 \end{array}$$ Find unbiased estimates of the population mean and variance of the weights of all 16 -year old males.
Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(\left(\frac{508}{8}\right) = 63.5\)B1
\((\Sigma x^2 = 32360.12)\)
\(\frac{8}{7}\left(\frac{32360.12}{8} - 63.5^2\right)\)M1 oe
\(= 14.6\) (3 sf) or \(2553/175\)A1 [3] From correct working 
## Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $\left(\frac{508}{8}\right) = 63.5$ | B1 | |
| $(\Sigma x^2 = 32360.12)$ | | |
| $\frac{8}{7}\left(\frac{32360.12}{8} - 63.5^2\right)$ | M1 | oe |
| $= 14.6$ (3 sf) or $2553/175$ | A1 [3] | From correct working |

---
1 The weights, in kilograms, of a random sample of eight 16-year old males are given below.

$$\begin{array} { l l l l l l l l } 
58.9 & 63.5 & 62.7 & 59.4 & 66.9 & 68.0 & 60.4 & 68.2
\end{array}$$

Find unbiased estimates of the population mean and variance of the weights of all 16 -year old males.

\hfill \mbox{\textit{CAIE S2 2016 Q1 [3]}}
This paper (7 questions)
View full paper
Q1 3 Q2 5 Q3 7 Q4 7 Q5 8 Q6 9 Q7 11