Task Sets: Interpreting Categorical and Quantitative Data - Common Core Math - HS Statistics and Probability

Work through problems with immediate feedback

Concepts

A coach has the 8 individual sprint times from one race and wants a
display that shows every athlete's exact time. Which plot is the best
choice?

A dot plot, because it preserves every individual value and suits
a small data set.

A histogram, because grouping the 8 times into bins shows the
shape best.

A box plot, because it summarizes the data with five numbers.

A bar graph, because the times are separate categories.

A distribution of household incomes is strongly right-skewed. Which
measures of center and spread are most appropriate to report?

Mean and standard deviation, because they use every value.

Mean and IQR, because the mean is the true center.

Median and IQR, because they resist the pull of the long tail.

Median and standard deviation, because the median is resistant.

A histogram has its tallest bars on the left and a long tail trailing
off toward the high values on the right. How is this distribution
described?

Left-skewed, because most of the data sits on the left.

Right-skewed, because skew is named for the direction of the tail.

Symmetric, because it has one clear peak.

Left-skewed, because the tail points away from the peak.

A scatter plot of a population over time curves upward ever more
steeply, doubling over roughly equal time intervals. Which model
family best fits this form?

Linear, because a line is the simplest model to fit.

Linear, because the points rise from left to right.

Quadratic, because any curve must be a parabola.

Exponential, because the values multiply by a roughly constant
factor over equal intervals.

After fitting a model, you make a residual plot. The residuals show a
clear U-shaped (curved) pattern around the zero line. What does this
tell you?

The fit is good, because the residuals stay near zero.

The data must contain an error, because residual plots should be
flat.

The model is the wrong family; a curved residual pattern signals a
poor fit.

Nothing useful; a residual plot should look like the scatter plot.

Two scatter plots are compared. Plot 1 has correlation coefficient
$r = 0.3$ ; Plot 2 has $r = -0.95$ . Which statement is correct?

Plot 1 shows the stronger association, because its $r$ is
positive.

Plot 2 shows the stronger linear association, because strength is
the magnitude of $r$ .

Plot 2 is weaker, because a negative $r$ is always weak.

They are equally strong, because $0.3$ and $-0.95$ are both
between $-1$ and $1$ .

A study finds that as monthly ice cream sales rise, monthly drowning
deaths also rise, with a strong positive correlation. What is the most
reasonable conclusion?

Eating ice cream causes drowning, because the correlation is
strong.

Drowning incidents cause people to buy more ice cream.

The correlation is fake and should be ignored.

A lurking variable (warm weather) likely drives both, so the
correlation does not show that one causes the other.

Procedures

For the data set $2, 4, 5, 7, 8, 10, 13$ , find the median.

In a survey, 40 students own a dog and 10 of those 40 dog owners also
own a cat. Among dog owners, what fraction also own a cat? Give a
decimal.

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HSS.ID Tutor Intake - Data Displays, Statistics, Models, and Correlation

Concepts

Procedures