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The lengths (in cm) of eight laboratory-grown seedlings are shown below.
- [1]
State whether “length” is a continuous or discrete variable.
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Write down the median length of the seedlings.
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Write down the range of the seedling lengths.
For these eight seedlings,
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find the mean length.
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write down the standard deviation.
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During a very difficult practice maths quiz, 40 high‑school students each received a mark out of 100.
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Write down the median mark.
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How many students scored 24 marks or less?
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How many students scored more than 29 marks?
A passing score is 27 marks.
- [3]
Determine the probability that a student scored above 29 marks given that they passed the exam.
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A school cafeteria manager surveyed students on how many days per week they buy lunch there. The results for a random sample are shown in the table below, where k is an unknown frequency:
It is known that the mean number of days per week a student buys lunch is 2.3.
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State whether this variable is discrete or continuous.
- [3]
Find the value of k.
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To select this sample, the manager listed all students by their student ID number and then asked every 8th student on the list to complete the survey. Identify the sampling technique used.
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The government of Mongolia surveys 6 herding families living in the valley of Yolyn to find out how many goats and sheep each family owns.
- [2]
Find and interpret Pearson's product-moment correlation coefficient, r, for this data.
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Find the equation of the regression line of s on g.
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Use the regression line found in (b) to predict the number of goats (g) owned by a family in the valley with 205 sheep (s).
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State two reasons why this prediction may not be accurate.
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A nutritionist records the amount of sugar (x, in grams) in ten different cereal brands and their average rating (y) given by a panel of tasters. The data are shown below.
- [2]
Use your calculator to calculate the Pearson product–moment correlation coefficient, r.
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Describe the correlation between sugar content and taste rating.
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Find the equation of the regression line of y on x, in the form y=mx+c.
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Estimate the expected taste rating when a cereal contains 15 grams of sugar.
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A health researcher measures each student’s average daily screen time x (in hours) and average nightly sleep y (in hours) for eight students:
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Use your calculator to find the Pearson product–moment correlation coefficient, r, to 3 significant figures.
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Find the equation of the regression line of y on x in the form y=mx+c.
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Use your regression line to estimate the average sleep for a student with x=5.5 hours of screen time.
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Interpret the value of r2 in the context of this study.
The researcher considers using the model to predict sleep for a student with x=10 hours of screen time.
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Comment on the suitability of this prediction.
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