VCAA General Mathematics Data analysis, probability and statistics

This option incorrectly uses the difference between the two given values ($3\sigma = 21.3$) as the standard deviation instead of dividing by 3 to find $\sigma$.

While the standard deviation of 7.1 is correct, the mean is miscalculated. The mean should be found by adding the standard deviation to 157.6.

This option incorrectly calculates the standard deviation as $2\sigma = 14.2$ and subsequently miscalculates the mean.

This reverses the variables; $R^2$ measures the proportion of variation in the response variable ($y$) explained by the explanatory variable ($x$), not the variation in $x$ explained by $y$.

$R^2$ measures the proportion of the variation in the observed response values ($y$), not the predicted outcomes, that is explained by the model.

This refers to the variation in the explanatory variable ($x$), whereas $R^2$ specifically measures the explained variation in the response variable ($y$).

This is the raw data value for Day 4, not the calculated moving average.

This value is incorrect; the average of the second window of data points (10, 18, and 32) is 20, not 25.

This is the raw data value for Day 3, not the calculated moving average.

Neither variable asks for a specific numerical measurement, such as an exact dollar amount. Since the responses are groups or labels, they are not numerical variables.

While payment preference is categorical, budget preference is also categorical because it groups responses into ranges ('less than ＄50' or 'more than ＄50') rather than asking for an exact numerical value.

Payment preference ('cash' or 'electronic') is clearly a categorical variable, not numerical. Budget preference is also categorical, making this option entirely incorrect.

A negative association requires a correlation coefficient less than zero ($r < 0$), but the given value is $0.23$.

A strong positive association typically corresponds to an $r$ value closer to $1$ (e.g., $r > 0.7$), whereas $0.23$ represents a weak relationship.

This option describes a correlation coefficient close to $-1$, but the given value is positive and indicates a weak relationship.

Incorrect. A 25% reduction would mean multiplying the actual sales by 0.75, which does not match the required deseasonalizing factor of $1/1.75 \approx 0.57$.

Incorrect. This is the percentage that the deseasonalized sales represent of the actual sales ($1/1.75 \approx 57\%$), rather than the percentage by which the actual sales must be reduced.

Incorrect. While a seasonal index of 1.75 means sales are 75% above the seasonal average, reversing this increase requires dividing by 1.75, not subtracting 75%.

This is an example of univariate data because it involves only one variable (the rating) for each observation.

This is univariate data because it records only a single variable (the count of cars) at a specific location.

This is univariate data because it measures only one variable (time spent) for each person observed.

This describes a discrete variable, which is defined by having a countable number of possible values, rather than a confounding variable.

A value that remains constant is simply a constant or a controlled variable, whereas a confounding variable varies and affects the outcome.

This describes the explanatory (or independent) variable, which is the specific factor the researcher is studying to see if it causes a change.

While the equation represents a linear relationship, a correlation coefficient of 0.92 indicates a strong association, not a weak one.

The equation $y = 4.6x - 35$ represents a linear relationship, and a correlation coefficient of 0.92 indicates a strong association, making both parts of this description incorrect.

Although the association is strong, the equation $y = 4.6x - 35$ is in the form $y = mx + c$, which models a linear relationship, not a non-linear one.

Incorrect. This value does not match the result of the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Incorrect. This is the reciprocal of the slope, incorrectly calculated by dividing the change in $x$ by the change in $y$ ($\frac{6.37}{-22.3} \approx -0.29$).

Incorrect. The data shows that as energy intake increases, birth rate decreases, meaning the slope must be negative.

Incorrect. This value is positive, but the inverse relationship between energy intake and birth rate requires a negative slope.