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Calculate relative frequencies in a variety of scenarios.

"}, "statement": "

The relative frequency of an outcome is the frequency of the outcome divided by the number of trials.

The relative frequency of an outcome is the frequency of the outcome divided by the number of trials.

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#### a)

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To calculate the relative frequency of people who performed static stretches we need the number of trials, which is $\\var{no_people}$, and the number of people who said that they they performed static stretches, which is $\\var{stretch}$.

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Therefore, the relative frequency of people who perform static stretches is

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\$\\frac{\\var{stretch}}{\\var{no_people}} = \\var{dpformat({stretch/no_people}, 2)} \\; (\\text{rounded to 2 decimal places}). \$

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#### b)

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We are told that the relative frequency of the number of femurs that break when $4000N$ is applied to them is $\\var{rel_freq}$, so we assume that the relative frequency is the same across all samples of femurs exposed to the same $4000N$ force. Therefore, in our sample of $\\var{no_students}$ femurs we expect that

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\\\begin{align} \\var{rel_freq} \\times \\var{no_students} = \\var{{rel_freq}*{no_students}} \\end{align} \

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femurs will break.

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As this result represents a number of femurs, if the answer is not an integer, we must round it to the nearest integer.

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#### c)

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i)

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Using the frequency table given in the question, we can calculate the sample size of the survey by adding together the frequencies of each of the different types of $3D$ motion analysis systems.

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So, the sample size of the survey is

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\$\\var{Vicon}+\\var{qualysis}+\\var{Optotrak} = \\var{Vicon + qualysis + Optotrak}. \$

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ii)

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To calculate the relative frequency of using Vicon as a type of $3D$ motion anaylsis system, we divide the frequency of Vicon by the sample size of the survey.

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So, the relative frequency is

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\$\\frac{\\var{Vicon}}{\\var{n}} = \\var{dpformat({Vicon/n}, 2)} \\; (\\text{rounded to 2 decimal places}). \$

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$\\var{no_people}$ track and field athletes were asked whether they perform static stretches before they competed. $\\var{stretch}$ athletes said that they performed static stretches.

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What is the relative frequency of athletes who perform static stretches before competing?

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You must give your answer as a decimal to 2 decimal places.

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The force required to break a femur during a simulated lateral fall was measured on multiple samples. The relative frequency of a femur breaking when $4000N$ was applied was estimated to be $\\var{rel_freq}$.

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Estimate the number of femurs that would break in a sample of $\\var{no_students}$ when a $4000N$ force is applied to them.

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A survey was conducted to find out what type of $3D$ motion analysis system is the most commonly used. The results are given in the table below.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
 Type of $3D$ motion anaylsis system Frequency Vicon $\\var{vicon}$ Qualysis $\\var{qualysis}$ Optotrak $\\var{optotrak}$
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i)

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What was the sample size for the survey?

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[[0]]

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ii)

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What is the relative frequency of using Vicon as a $3D$ motion analysis system?

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[[1]]

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Frequency of cat in part c.

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Frequency of hamster in part c

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Number of people asked in part a)

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Number of people who prefer free-range eggs in part a)

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Sample size for part c

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Relative frequency for part b

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Number of students in the class for part b

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