Math Repository
about
topic
al
year
ly
Yearly
2013
P2 Q9
Topical
Sampling
13 P2 Q9
2013 H2 Mathematics Paper 2 Question 9
Sampling Theory
Answers
(i)
Unbiased estimate of mean of population mean
=
12.8
{= 12.8}
=
12.8
Unbiased estimate of variance of population variance
=
2.31
{= 2.31}
=
2.31
(ii)
Out of syllabus
Full solutions
(i)
Unbiased estimate of population mean
=
x
‾
=
∑
x
n
=
102.4
8
=
12.8
■
\begin{align*} & \textrm{Unbiased estimate of population mean} \\ & = \overline{x} \\ & = \frac{\sum x}{n} \\ & = \frac{102.4}{8} \\ & = 12.8 \; \blacksquare \end{align*}
Unbiased estimate of population mean
=
x
=
n
∑
x
=
8
102.4
=
12.8
■
Unbiased estimate of variance of
X
=
s
2
=
1
n
−
1
(
∑
x
2
−
(
∑
x
)
2
n
)
=
1
8
−
1
(
1326.86
−
(
102.4
)
2
8
)
=
2.31
(3 sf)
■
\begin{align*} & \textrm{Unbiased estimate of variance of } X \\ & = s^2 \\ & = \frac{1}{n-1}\left( \sum x^2 - \frac{\left(\sum x\right)^2}{n} \right) \\ & = \frac{1}{8-1}\left( 1326.86 - \frac{\left(102.4\right)^2}{8} \right) \\ & = 2.31 \textrm{ (3 sf)} \; \blacksquare \end{align*}
Unbiased estimate of variance of
X
=
s
2
=
n
−
1
1
(
∑
x
2
−
n
(
∑
x
)
2
)
=
8
−
1
1
(
1326.86
−
8
(
102.4
)
2
)
=
2.31
(3 sf)
■
(ii)
Out of syllabus
Back to top ▲