C883 Statistics and Probability for Secondary Mathematics Teaching
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Free C883 Statistics and Probability for Secondary Mathematics Teaching Questions
A teacher finds r = 0.95 between hours studied and test score. To avoid claiming causation, the lesson should emphasize:
- Correlation ≠ causation
- Strong causation exists
- Extrapolation is safe
- Remove outliers
Explanation
A high correlation indicates a strong linear relationship but does not prove that one variable causes the other. Other factors or lurking variables may explain the association. Teaching students that correlation does not imply causation is essential to prevent misinterpretation of data.
Correct Answer:
Correlation ≠ causation
Which sampling method is most likely to produce bias when surveying teens about social media use?
- Simple random sampling
- Stratified sampling
- Online poll on Instagram
- Cluster sampling
Explanation
An online poll on Instagram is likely to produce bias because it only reaches teens who use Instagram and are willing to respond. This self-selection excludes teens who do not use the platform or choose not to participate, leading to unrepresentative results. Teaching students about this helps them understand how sampling methods affect the reliability of survey data.
Correct Answer:
Online poll on Instagram
In a scatterplot, an outlier pulls the regression line toward it, causing:
- Underestimation of slope
- Overestimation of slope
- No effect
- Perfect fit
Explanation
Outliers can disproportionately influence the slope and intercept of a regression line. Depending on its position relative to the main cluster of points, an outlier can either increase or decrease the slope. This demonstrates to students the importance of detecting outliers and understanding their effect on regression analysis.
Correct Answer:
Overestimation of slope
Which data display is best for showing change over time in student performance?
- Bar graph
- Line graph
- Pie chart
- Histogram
Explanation
A line graph is most appropriate for displaying change over time because it connects data points in a sequence, making trends, increases, and decreases easily visible. In the context of student performance, a line graph allows teachers and students to track progress across multiple assessments or time periods, clearly illustrating patterns and growth over time.
Correct Answer:
Line graph
The slope of the regression line y = 3.2x + 15 means:
- For each 1-unit increase in x, y increases by 15
- For each 1-unit increase in x, y increases by 3.2
- Intercept is 3.2
- Correlation is 3.2
Explanation
In the regression equation y = mx + b, the slope m represents the change in y for a one-unit increase in x. Here, a slope of 3.2 means that for each additional unit of x, y increases by 3.2 units. Teaching slope interpretation helps students understand the quantitative relationship between variables in linear regression.
Correct Answer:
For each 1-unit increase in x, y increases by 3.2
Without replacement from the same bag, P(first red and second blue) =
- 15/56
- 15/64
- 5/14
- 3/14
Explanation
Without replacement, the probabilities change after the first draw. The probability of drawing a red marble first is 5/8. After removing one red marble, there are 7 marbles left, with 3 blue marbles. The probability of drawing a blue marble second is 3/7. Multiplying these together gives (5/8) × (3/7) = 15/56. This demonstrates how probabilities adjust when events are dependent.
Correct Answer:
15/56
A teacher flips two coins. The sample space has how many equally likely outcomes?
- 2
- 3
- 4
- 6
Explanation
Flipping two coins results in all possible ordered outcomes: HH, HT, TH, TT. There are 4 equally likely outcomes, which form the sample space. Understanding sample space is essential for calculating probabilities and visualizing all possible events in a scenario.
Correct Answer:
4
Using the tree above, P(sandwich and juice) =
- 0.42
- 0.70
- 0.60
- 0.18
Explanation
To find the probability of sequential independent events, multiply the probabilities along the corresponding path. For sandwich (0.6) and juice (0.7), P(sandwich and juice) = 0.6 × 0.7 = 0.42. This demonstrates how tree diagrams can be used to calculate joint probabilities for multiple events.
Correct Answer:
0.42
To teach fairness, a game is fair if expected value =
- 0
- Positive
- Negative
- 1
Explanation
A fair game is one in which the expected value of playing is zero, meaning that over many repetitions, a player neither gains nor loses on average. This concept helps students understand how probability and expected value relate to fairness in games and real-world scenarios.
Correct Answer:
0
A teacher calculates MAD (mean absolute deviation) to show:
- Average distance from mean
- Squared distances
- From median
- For categorical data
Explanation
Mean absolute deviation (MAD) measures the average distance of each data point from the mean, using absolute values to avoid cancellation of positive and negative deviations. It provides a clear and intuitive sense of variability in a data set, making it useful for teaching students how spread out the data are around the mean.
Correct Answer:
Average distance from mean
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