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Answer the following questions on the sampling methods used in these situations.
Identify each of the following scenarios as one of the following:
Note that you will lose 1 mark for every incorrect answer, however the least mark for this part of the question is 0.
There's nothing more to do from here.
For each choice, state whether the form of the sampling described is random, quasi-random or non-random.
As before, you will lose 1 mark for every incorrect answer, however the least mark for this part of the question is 0.
There's nothing more to do from here.
The following table shows daily sales, $X$, in thousands of pounds for a large retailer in 2010.
Calculate the relative percentage frequencies (to one decimal place for all).
Sales | Number of days | Relative Percentages |
---|---|---|
$\var{a[0]}\le X \lt \var{a[1]}$ | $\var{norm1[0]}$ | question.score feedback.none |
$\var{a[1]}\le X \lt \var{a[2]}$ | $\var{norm1[1]}$ | question.score feedback.none |
$\var{a[2]}\le X \lt \var{a[3]}$ | $\var{norm1[2]}$ | question.score feedback.none |
$\var{a[3]}\le X \lt \var{a[4]}$ | $\var{norm1[3]}$ | question.score feedback.none |
$\var{a[4]}\le X \lt \var{a[5]}$ | $\var{norm1[4]}$ | question.score feedback.none |
$\var{a[5]}\le X \lt \var{a[6]}$ | $\var{norm1[5]}$ | question.score feedback.none |
$\var{a[6]}\le X \lt \var{a[7]}$ | $\var{norm1[6]}$ | question.score feedback.none |
There's nothing more to do from here.
We show how to calculate the relative percentage frequency for one range of values for $\var{a[r]} \le X \lt \var{a[r+1]}$ - you can then check the rest.
Note that there were $\var{daysopen}$ days in the year when sales took place.
There were $\var{norm1[r]}$ days out of the $\var{daysopen}$ when there were between $\var{a[r]}$ and $\var{a[r+1]}$ thousand pounds worth of sales (including $\var{a[r]}$ thousand but not $\var{a[r+1]}$ thousand) .
Hence the relative frequency percentage for such sales is given by \[100 \times \frac{\var{norm1[r]}}{\var{daysopen}}\%=\var{rel[r]}\%\] to one decimal place.
The following data are the number of orders per month for specialist camera equipment, over a 2 year period, taken by an online warehouse
J | F | M | A | M | J | J | A | S | O | N | D | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Year 1: | 7 | 13 | 11 | 8 | 12 | 14 | 14 | 15 | 7 | 6 | 12 | 5 |
Year 2: | 8 | 12 | 11 | 6 | 12 | 14 | 13 | 12 | 8 | 7 | 16 | 6 |
Answer the following questions:
Sample mean = question.score feedback.noneorders. Give your answer to $2$ decimal places.
Sample Standard Deviation = question.score feedback.none orders. Give your answer to $2$ decimal places.
Sample Median = question.score feedback.none (Input as an exact decimal).
The interquartile range= question.score feedback.none (Input as an exact decimal).
There's nothing more to do from here.
As we have to find the median and the interquartile range it is a good idea to order the data and also to total up the data (for the mean) and find the total of the squares of the data (for the variance).
Data | 5 | 6 | 6 | 6 | 7 | 7 | 7 | 8 | 8 | 8 | 11 | 11 | 12 | 12 | 12 | 12 | 12 | 13 | 13 | 14 | 14 | 14 | 15 | 16 |
Squared data | 25 | 36 | 36 | 36 | 49 | 49 | 49 | 64 | 64 | 64 | 121 | 121 | 144 | 144 | 144 | 144 | 144 | 169 | 169 | 196 | 196 | 196 | 225 | 256 |
Index | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
Note that from the above table:
$n=\var{m*n}$.
$\displaystyle \sum x_i = \var{sum(r)}$ and
$\displaystyle \sum x^2_i = \var{sum(map(x^2,x,r))}$ .
The sample mean is $\bar{x}=\displaystyle \frac{ \sum x_i}{n}=\frac{\var{sum(r)}}{\var{m*n}}=\var{mean(r)}=\var{av}$ to 2 decimal places.
The sample deviation is the square root of the sample variance.
Sample variance:\[\begin{eqnarray*}\frac{1}{ n -1}\left(\sum x_i ^ 2 - n \bar{x} ^ 2\right)&=& \frac{1}{\var{m*n-1}}\left(\var{sum(map(x^2,x,r))}-\var{m*n}\times\var{mean(r)^2}\right)\\&=&\var{variance(r,true)}\end{eqnarray*}\] Note that we used the more accurate value $(\var{mean(r)})^2$ for $\bar{x}^2$.
So the sample standard deviation = $\sqrt{\var{variance(r,true)}}=\var{std}$ to 2 decimal places.
The median is $\var{median(r)} $.
The lower quartile is : $\var{lquartile(r)}$.
The upper quartile is : $\var{uquartile(r)}$.
The interquartile range is the difference between these quartiles =$\var{uquartile(r)}-\var{lquartile(r)}=\var{uquartile(r)-lquartile(r)}$