Easy -1.2 This is a straightforward calculation requiring only direct application of standard formulas for sample mean and unbiased variance (dividing by n-1). No problem-solving, conceptual understanding, or multi-step reasoning required—purely mechanical computation with small dataset.
1 The weights, in grams, of a random sample of 8 packets of cereal are as follows.
$$\begin{array} { l l l l l l l l }
250 & 248 & 255 & 244 & 259 & 250 & 242 & 258
\end{array}$$
Calculate unbiased estimates of the population mean and variance.
\(\frac{\Sigma x}{8} = \frac{2006}{8} = 250.75\) or \(251\) (3 s.f.)
B1
(\(\Sigma x^2 = 503274\))
Answer
Marks
Guidance
\(\sqrt{\frac{503274}{8} - 250.75^2}\) or \(\sqrt{\frac{503274 - 8 \times 250.75^2}{8}}\)
M1
Any equivalent form, for use of formula of correct form
\(= 38.5\) o.e. (accept \(6.204^2\))
A1
cao (as final answer)
[3]
Question 1:
$\Sigma x = 2006$
$\frac{\Sigma x}{8} = \frac{2006}{8} = 250.75$ or $251$ (3 s.f.) | B1
($\Sigma x^2 = 503274$)
$\sqrt{\frac{503274}{8} - 250.75^2}$ or $\sqrt{\frac{503274 - 8 \times 250.75^2}{8}}$ | M1 | Any equivalent form, for use of formula of correct form
$= 38.5$ o.e. (accept $6.204^2$) | A1 | cao (as final answer)
[3]
1 The weights, in grams, of a random sample of 8 packets of cereal are as follows.
$$\begin{array} { l l l l l l l l }
250 & 248 & 255 & 244 & 259 & 250 & 242 & 258
\end{array}$$
Calculate unbiased estimates of the population mean and variance.
\hfill \mbox{\textit{CAIE S2 2014 Q1 [3]}}