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Statistics, STD2 2026 HSC 16

A coach was interested in whether there was a relationship between the number of hours spent practising kicking a ball and the number of goals scored in a competition.

The coach collected data from 10 players. A graph of the dataset is shown.

  1. Describe the bivariate dataset in terms of its form, direction and strength.   (3 marks)
  2. Form: ..............................................................
  3. Direction: ........................................................
  4. Strength: .........................................................
  5. The line of best fit has equation  \(y=2.8+0.4x\).
  6. Using this equation, what is the expected number of goals scored by a player who spent 5 hours practising kicking a ball?   (1 mark)
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a.    \(\text{Linear, positive, strong}\)

b.    \(\text{4.8 goals}\)

Show Worked Solution

a.    \(\text{Form: linear}\)

\(\text{Direction: positive}\)

\(\text{Strength: strong}\)
 

b.    \(y=2.8+0.4(5)=4.8\ \text{goals}\)

Statistics, STD2 S4 2024 HSC 30

A researcher is studying anacondas (a type of snake).

A dataset recording the age (in years) and length (in cm) of female and male anacondas is displayed on the graph.

Anacondas reach maturity at about 4 years of age.
 

Write THREE observations about anacondas that may be made from the scatterplot. (Note: No calculations are required.)   (3 marks)

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\(\text{Answers could include three of the following:}\)

\(\rightarrow\ \text{Female anacondas are longer than males of the equivalent age.}\)

\(\rightarrow\ \text{Female anacondas grow more quickly than male anacondas from birth until}\)

\(\text{maturity which can be seen by the steeper gradient of the LOBF for each dataset}\)

\(\text{over this period.}\)

\(\rightarrow\ \text{Female anacondas continue to grow to at least 10 years of age, well past their}\)

\(\text{age of maturity at 4 years of age.}\)

\(\rightarrow\ \text{Male anacondas’ growth slows noticeably and flattens out once they hit their}\)

\(\text{age of maturity at 4 years old.}\)

Show Worked Solution

\(\text{Answers could include three of the following:}\)

\(\rightarrow\ \text{Female anacondas are longer than males of the equivalent age.}\)

\(\rightarrow\ \text{Female anacondas grow more quickly than male anacondas from birth until}\)

\(\text{maturity which can be seen by the steeper gradient of the LOBF for each dataset}\)

\(\text{over this period.}\)

\(\rightarrow\ \text{Female anacondas continue to grow to at least 10 years of age, well past their}\)

\(\text{age of maturity at 4 years of age.}\)

\(\rightarrow\ \text{Male anacondas’ growth slows noticeably and flattens out once they hit their}\)

\(\text{age of maturity at 4 years old.}\)