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Find the means of the following sets of numbers. Enter your answers as whole numbers or fractions, not decimals.

a)

5,5,2

Expected answer:

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b)

5,5,12,2,13

Expected answer:

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Advice

a)

To find the mean you first need to sum the numbers, i.e.:

5+5+2=12

Then divide through by the number of values being summed:

Mean=4

b)

The mean is

5+5+12+2+135=375

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Find the medians of the following sets of numbers. Enter your answers as whole numbers or fractions, not decimals.

a)

$\var{v_less_9a},\var{v_more_11a},\var{v_less_9b},\var{v_between_9_11},\var{v_more_11b}$.

Expected answer:

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b)

$\var{v_less_4a}, \var{v_less_4b}, \var{v_between_5_10},\var{v_more_10a}, \var{v_more_10b}$

Expected answer:

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Advice

a)

First, put the elements in increasing order, i.e.

\[ \var{latex(join(sort([v_less_9a,v_more_11a,v_less_9b,v_between_9_11,v_more_11b]),','))} \]

The median of the set is the middle value in the sorted list. In this case, it's $\var{v_between_9_11}$.

b)

First, put the elements in increasing order, i.e.

\[ \var{latex(join(sort([v_less_4a,v_less_4b,v_between_5_10,v_more_10a,v_more_10b]),','))} \]

The median of the set is the middle value in the sorted list. In this case, it's $\var{v_between_5_10}$.

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Find the mode of each list of numbers.

a)

87581419

Expected answer:

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b)

6112081613161610

Expected answer:

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Advice

a)

The mode is the value which appears the most often in the data set.

It can help to put the values in order:

57881419

The mode of these numbers is $\var{mode1}$.

b)

Similarly, it can help to first put the values in order:

6810111316161620

The mode of these numbers is $\var{mode2}$.

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Using the definition of the range to answer the following questions

a)

The amount of drugs the doctor prescribed this month has a maximum weight of $\var{max_drugs}$g and has a range of $\var{range_drugs}$g. What is the minimum weight the doctor prescribed this month?

Expected answer: g

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b)

A pharmacy has a variable amount of Dittany in stock at any one point. When the stock gets down to $\var{min_bottles}$ they must order more. Each order comes with $\var{shipment}$ bottles. What is the range of the number of bottles of Dittany in stock?

Range: Expected answer:  bottles.

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Advice

The range of a set of data is defined to be the difference between the greatest value and the least value.

E.g. the set $2, 3, 4, 4, 7$ has a range of 5 since $7-2=5$.

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A recent survey asked people "How long do you spend relaxing each day? For example wating TV, reading, or listening to the radio."

The survey received $\var{people}$ responses with a mean of $\var{average}$ hours and a standard deviation of $\var{sd}$ hours.

What is the standard error of the sample mean? Round your answer to 3 decimal places.

Expected answer:

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Advice

The standard error of the sample mean is given by 

\[ \text{Standard error} = \frac{s}{\sqrt{n}} \]

where $s$ is the sample standard deviation, and $n$ is the size of the sample.

In this case, the standard error is

\[ \simplify{{sd}/sqrt({people})} = \var{dpformat(se,3)} \text{ (to 3 d.p.)} \]

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Joe makes a variable number of visits to the toilet each day. He recorded his activities as follows:

MondayTuesdayWednesdayThursdayFridaySaturdaySunday
4414422

Compute the following descriptive statistics of the data. Round your answers to 2 decimal places.

a)

Mean: Expected answer:

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b)

Range:  Expected answer:

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c)

Variance: Expected answer:

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Advice

a)

The mean of a set of data is the sum of the data, divided by the number of values in the set. In this case, the mean is

\[ \simplify[]{({mon}+{tues}+{wed}+{thurs}+{fri}+{sat}+{sun})/7} = \var{precround(mean,2)} \text{ (to 2 d.p.)}\]

b)

The range of a set of data is the difference between the greatest and least values in the set. In this case, the range is

\[ \simplify[]{{max(data)}-{min(data)} = {range}} \]

c)

The variance of a sample $x_1,x_2, \dots, x_n$ is given by the following formula:

\[ \text{Variance} = \sum \frac{(x_i-\mu)^2}{n}\]

$x_i$4414422
$x_i-\mu$11-211-1-1
$(x_i-\mu)^2$1141111

Now,

\[ \text{Variance} = \frac{1}{7} \sum (x_i-\mu)^2 = \var{precround(variance,2)} \text{ (to 2 d.p.)} \]

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