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PSAT/NMSQT Math / LEVEL 3 · DIFFICULTY 3/5

Data Analysis: Evidence & Predictions

Use data displays, probability, sampling, rates and units to reason carefully.

6 stages · 48 practice problems · two 12-question assessment forms

Choose a node to explore its lesson.

STAGE PSAT 3.1 · 8 PRACTICE PROBLEMS · 4 NEW-CONTEXT APPLICATIONS

Standard Deviation, Center & Outliers

Goal: Compare variability, predict how shifts and scaling affect spread, and distinguish effects on mean and median.

Before you begin: Read the problem carefully and use the linked foundation lessons when a term or operation is unfamiliar.

Move the dots. Watch the spread.

This is an exploration example. Its values are separate from your practice question.

Spread factor: 1Shift every value: +0

Values: 2, 3, 3, 4, 4, 4, 5, 5, 6. Mean = 4; population standard deviation ≈ 1.15.

Shifting changes the center but keeps the spread. Stretching around the center changes spread but keeps the mean.

Make sense of the idea

Standard deviation describes how far values typically lie from their mean. A tightly packed set has smaller standard deviation than a more spread-out set with the same center. You usually can compare without calculating a formula.

Choose a method

Adding the same constant to every value shifts the mean and median but leaves standard deviation unchanged. Multiplying every value by c multiplies standard deviation by $\displaystyle \left|c\right|$ .

Check and interpret

An extreme outlier can pull the mean strongly. The median depends on ordered position and is often less affected. Always compare center and spread separately.

WORKED EXAMPLE 1

Compare $\displaystyle A : 6$ , 7, 8; $\displaystyle B : 4$ , 7, 10. Which has greater standard deviation? Enter 1 for A, 2 for B, or 3 if equal.

Both means are 7. A has distances 1, 0, 1; B has distances 3, 0, 3.
B is more spread out and has 3 times the standard deviation. Enter 2.

WORKED EXAMPLE 2

Five commute times are 6, 7, 8, 9, 10. Only the largest value is replaced by 56. What is the new median?

The third value is still 8.
So the median remains 8, although the mean and spread increase.

Common pitfalls

Possible mix-up: A larger mean always means more spread.

Shifting all observations changes the mean without changing spread.

Possible mix-up: Adding 5 to each value adds 5 to the standard deviation.

All distances from the mean stay the same.

Explain it to yourself

In standard deviation, center & outliers, what information determines your method, and how can you check whether your result fits the original conditions?

Preview the eight practice prompts

Problem 1
Compare $\displaystyle A : 4$ , 5, 6; $\displaystyle B : 2$ , 5, 8. Which has greater standard deviation? Enter 1 for A, 2 for B, or 3 if equal.
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Problem 2
Every observation in a data set is increased by 9. The original standard deviation is 2. What is the new standard deviation?
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Problem 3
A transformation multiplies every data value by 3. If the original standard deviation is 2, what is the new standard deviation?
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Problem 4
A sorted data set is 3, 4, 5, 6, 7. Only the largest value is replaced by 53. What is the new median?
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Problem 5New context
Two teams record $\displaystyle A : 5$ , 6, 7; $\displaystyle B : 3$ , 6, 9. Which has greater standard deviation? Enter 1 for A, 2 for B, or 3 if equal.
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Problem 6New context
Every temperature reading is increased by 10. The original standard deviation is 3. What is the new standard deviation?
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Problem 7New context
A measurement unit conversion multiplies every data value by 3. If the original standard deviation is 3, what is the new standard deviation?
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Problem 8New context
Five commute times are 4, 5, 6, 7, 8. Only the largest value is replaced by 54. What is the new median?
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Open stage PSAT 3.1 in the student workspace →

STAGE PSAT 3.2 · 8 PRACTICE PROBLEMS · 4 NEW-CONTEXT APPLICATIONS

Dot Plots, Histograms & Frequency Tables

Goal: Read frequencies and intervals, locate medians from counts, and distinguish what grouped data can and cannot tell you.

Before you begin: Read the problem carefully and use the linked foundation lessons when a term or operation is unfamiliar.

Same observations, different displays

This is an exploration example. Its values are separate from your practice question.

Spread factor: 1Shift every value: +0Display

Values: 2, 3, 3, 4, 4, 4, 5, 5, 6. Mean = 4; population standard deviation ≈ 1.15.

Shifting changes the center but keeps the spread. Stretching around the center changes spread but keeps the mean.

A histogram groups these observations into intervals
Interval	Frequency
0 ≤ value < 4	3
4 ≤ value < 8	6
8 ≤ value < 12	0

Moving a value across an interval boundary changes its bin. The histogram gives counts, but hides exact positions within each bin.

Make sense of the idea

In a dot plot each dot is one observation. Repeated values form stacks. A frequency table records the same information with counts.

Choose a method

A histogram groups numerical values into nonoverlapping intervals. The height gives frequency, not the data value. Read interval endpoints carefully: [10,20) includes 10 but excludes 20.

Check and interpret

Use cumulative counts to locate the median. From grouped counts alone you can identify a median interval, but generally cannot reconstruct an exact mean or each original observation.

WORKED EXAMPLE 1

A frequency table lists score $\displaystyle 4 : 2$ observations; score $\displaystyle 5 : 3$ observations; score $\displaystyle 6 : 1$ observation. What is the mean score?

The total count is $\displaystyle 2 + 3 + 1 = 6$ .
The sum is $\displaystyle 2 \times 4 + 3 \times 5 + 6 = 29$ , so the mean is $\displaystyle \frac{29}{6}$ .

$\displaystyle \frac{29}{6}$

WORKED EXAMPLE 2

A delivery-time histogram contains 8 values in [0,10), 10 in [10,20), and 1 in [20,30). Can the EXACT mean be determined from these counts alone? Enter 1 for yes or 0 for no.

Histogram: intervals include the left endpoint and exclude the right

Different raw data sets can produce exactly these same bin counts.
Their sums, and hence means, can differ. The exact mean is not determined; enter 0.

Common pitfalls

Possible mix-up: A bar height is the measurement value.

The horizontal axis gives values or intervals; the height gives frequency.

Possible mix-up: A histogram gives an exact value for each observation.

Grouping loses information within each bin.

Explain it to yourself

In dot plots, histograms & frequency tables, what information determines your method, and how can you check whether your result fits the original conditions?

Preview the eight practice prompts

Problem 1
A frequency table lists score $\displaystyle 2 : 2$ observations; score $\displaystyle 3 : 3$ observations; score $\displaystyle 4 : 1$ observation. What is the mean score?
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Problem 2
A dot plot has 2 dots at 3, 3 at 5, and 2 at 8. What is the median?
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Problem 3
A histogram has 4 observations in [0,10), 6 in [10,20), and 8 in [20,30). How many observations are at least 10?
Histogram: intervals include the left endpoint and exclude the right
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Problem 4
A histogram contains 5 values in [0,10), 7 in [10,20), and 1 in [20,30). Can the EXACT mean be determined from these counts alone? Enter 1 for yes or 0 for no.
Histogram: intervals include the left endpoint and exclude the right
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Problem 5New context
A reading $\displaystyle \operatorname{log}$ lists score $\displaystyle 3 : 2$ observations; score $\displaystyle 4 : 3$ observations; score $\displaystyle 5 : 1$ observation. What is the mean score?
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Problem 6New context
A dot plot of daily visits has 2 dots at 4, 3 at 6, and 2 at 9. What is the median?
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Problem 7New context
A histogram of wait times has 5 observations in [0,10), 7 in [10,20), and 9 in [20,30). How many observations are at least 10?
Histogram: intervals include the left endpoint and exclude the right
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Problem 8New context
A delivery-time histogram contains 6 values in [0,10), 8 in [10,20), and 1 in [20,30). Can the EXACT mean be determined from these counts alone? Enter 1 for yes or 0 for no.
Histogram: intervals include the left endpoint and exclude the right
Practise this exact problem →

Open stage PSAT 3.2 in the student workspace →

STAGE PSAT 3.3 · 8 PRACTICE PROBLEMS · 4 NEW-CONTEXT APPLICATIONS

Scatterplots & Lines of Best Fit

Goal: Describe scatterplot trends, use a fitted line to predict, interpret residuals, and compare linear with exponential patterns.

Before you begin: Read the problem carefully and use the linked foundation lessons when a term or operation is unfamiliar.

A fitted line follows the pattern

Five observations, with a least-squares fitted line $\displaystyle y = 1.2\, x + 1$ . Drag the input control to predict a value.

Predict at

\displaystyle x = 3

Fitted line

0012243648510612714816xy

Predicted y = 4.6. This input is within the observed range: interpolation.

At $\displaystyle x = 3$ , the observed value is 4 and the prediction is 4.6. Residual = $\displaystyle 4 - 4.6 = -0.6$ : that dot is below the fitted line.

Read the paired observations

x	Observed y	Predicted y
1	2	2.2
2	4	3.4
3	4	4.6
4	6	5.8
5	7	7

Make sense of the idea

Each scatterplot point is one paired observation (x,y). A positive trend rises overall as x increases; it does not require every point to lie exactly on a line.

Choose a method

A fitted line follows the overall pattern and balances deviations; it need not pass through the origin or every point. In y = mx + b, m is the predicted change in y for one extra x-unit.

Check and interpret

A residual is observed y minus predicted y. Prediction within the observed x-range is interpolation; going outside it is extrapolation and needs caution. Equal differences suggest a linear pattern; equal positive ratios suggest an exponential one.

WORKED EXAMPLE 1

A fitted line is $\displaystyle y = 4\, x + 7$ . What y-value does it predict at $\displaystyle x = 4$ ?

ŷ = $\displaystyle 4 \times 4 + 7$ .
The predicted value is 23; an actual observation may differ.

WORKED EXAMPLE 2

A scatterplot model was built using x-values from 6 to 16. Predicting at $\displaystyle x = 26$ is which type? Enter 1 for interpolation or 2 for extrapolation.

26 is larger than the observed maximum 16.
This is extrapolation (2); the same trend may not continue outside the observed range.

Common pitfalls

Possible mix-up: A best-fit line must pass through every point.

Real data usually scatter around it.

Possible mix-up: A positive residual means the model predicted too much.

It means the observation is above the prediction.

Explain it to yourself

In scatterplots & lines of best fit, what information determines your method, and how can you check whether your result fits the original conditions?

Preview the eight practice prompts

Problem 1
A fitted line is $\displaystyle y = 2\, x + 5$ . What y-value does it predict at $\displaystyle x = 4$ ?
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Problem 2
A fitted model is $\displaystyle y = 3\, x + 6$ . At $\displaystyle x = 4$ , the observed y is 20. Find the residual (observed minus predicted).
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Problem 3
A data table has $\displaystyle x = 0$ ,1,2,3 and $\displaystyle y = 2$ ,4,8,16. Which model fits this exact pattern: 1 for linear or 2 for exponential?
Paired observations from this question
x 0 1 2 3
y 2 4 8 16
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Problem 4
A fitted line was built using x-values from 3 to 13. Predicting at $\displaystyle x = 23$ is which type? Enter 1 for interpolation or 2 for extrapolation.
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Problem 5New context
A scatterplot of study time and practice scores has fitted line $\displaystyle y = 3\, x + 6$ . What y-value does it predict at $\displaystyle x = 4$ ?
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Problem 6New context
A delivery-time model is $\displaystyle y = 3\, x + 7$ . At $\displaystyle x = 4$ , the observed y is 21. Find the residual (observed minus predicted).
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Problem 7New context
A growth record has $\displaystyle x = 0$ ,1,2,3 and $\displaystyle y = 3$ ,6,12,24. Which model fits this exact pattern: 1 for linear or 2 for exponential?
Paired observations from this question
x 0 1 2 3
y 3 6 12 24
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Problem 8New context
A scatterplot model was built using x-values from 4 to 14. Predicting at $\displaystyle x = 24$ is which type? Enter 1 for interpolation or 2 for extrapolation.
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x	0	1	2	3
y	2	4	8	16

x	0	1	2	3
y	3	6	12	24

Open stage PSAT 3.3 in the student workspace →

STAGE PSAT 3.4 · 8 PRACTICE PROBLEMS · 4 NEW-CONTEXT APPLICATIONS

Two-Way Tables & Conditional Probability

Goal: Use a two-way frequency table to choose the correct denominator for joint, marginal and conditional probabilities.

Before you begin: Read the problem carefully and use the linked foundation lessons when a term or operation is unfamiliar.

First choose who can be selected

Probability question

How 20 club members travel
Club	Bus	Walk	Total
A	6	4	10
B	3	7	10
Total	9	11	20

Only the 10 club A members can be selected. Probability = $\displaystyle \frac{6}{10}$ .

The phrase “given” changes the denominator. The table itself has not changed.

Make sense of the idea

A two-way table classifies each person by two categories. Each inner cell belongs to one row and one column. Row and column totals are marginal counts.

Choose a method

A joint probability asks for both properties: use the intersection cell divided by the grand total. A marginal probability uses a row or column total divided by the grand total.

Check and interpret

A conditional probability restricts the sample space first. “Given the person is in Group A” means divide by the Group A total, not by all people. Reverse conditions generally give different probabilities.

WORKED EXAMPLE 1

A two-way table gives club A: bus 4, walk 6; club B: bus 5, walk 7. Given a student is in club A, what is the probability they take the bus? Enter a fraction.

The counts from this question
Club	Bus	Walk	Total
A	4	6	10
B	5	7	12
Total	9	13	22

Club A contains 10 students and 4 take the bus.
The conditional probability is $\displaystyle \frac{4}{10}$ .

$\displaystyle \frac{4}{10}$

WORKED EXAMPLE 2

A transport survey gives club A: bus 8, walk 6; club B: bus 5, walk 7. Given that a student takes the bus, what is the probability they are in club A?

The counts from this question
Club	Bus	Walk	Total
A	8	6	14
B	5	7	12
Total	13	13	26

The bus group has 13 students, of whom 8 are in club A.
P(A given bus) = $\displaystyle \frac{8}{13}$ .

$\displaystyle \frac{8}{13}$

Common pitfalls

Possible mix-up: Every probability uses the grand total.

Conditional probability uses the total of the given group.

Possible mix-up: P(A given B) equals P(B given A).

Their denominators differ unless special counts happen to make them equal.

Explain it to yourself

In two-way tables & conditional probability, what information determines your method, and how can you check whether your result fits the original conditions?

Preview the eight practice prompts

Problem 1
A two-way table gives club A: bus 2, walk 4; club B: bus 3, walk 5. Given a student is in club A, what is the probability they take the bus? Enter a fraction.
The counts from this question
Club Bus Walk Total
A 2 4 6
B 3 5 8
Total 5 9 14
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Problem 2
A two-way table gives club A: bus 3, walk 4; club B: bus 6, walk 5. A student is selected from ALL students. What is the probability of club B AND walking?
The counts from this question
Club Bus Walk Total
A 3 4 7
B 6 5 11
Total 9 9 18
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Problem 3
A two-way table gives club A: bus 4, walk 2; club B: bus 3, walk 6. What is the probability a randomly selected student walks, regardless of club?
The counts from this question
Club Bus Walk Total
A 4 2 6
B 3 6 9
Total 7 8 15
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Problem 4
A two-way table gives club A: bus 5, walk 3; club B: bus 2, walk 4. Given that a student takes the bus, what is the probability they are in club A?
The counts from this question
Club Bus Walk Total
A 5 3 8
B 2 4 6
Total 7 7 14
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Problem 5New context
A survey gives club A: bus 3, walk 5; club B: bus 4, walk 6. Given a student is in club A, what is the probability they take the bus? Enter a fraction.
The counts from this question
Club Bus Walk Total
A 3 5 8
B 4 6 10
Total 7 11 18
Practise this exact problem →
Problem 6New context
A travel survey gives club A: bus 4, walk 5; club B: bus 7, walk 6. A student is selected from ALL students. What is the probability of club B AND walking?
The counts from this question
Club Bus Walk Total
A 4 5 9
B 7 6 13
Total 11 11 22
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Problem 7New context
A school survey gives club A: bus 5, walk 3; club B: bus 4, walk 7. What is the probability a randomly selected student walks, regardless of club?
The counts from this question
Club Bus Walk Total
A 5 3 8
B 4 7 11
Total 9 10 19
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Problem 8New context
A transport survey gives club A: bus 6, walk 4; club B: bus 3, walk 5. Given that a student takes the bus, what is the probability they are in club A?
The counts from this question
Club Bus Walk Total
A 6 4 10
B 3 5 8
Total 9 9 18
Practise this exact problem →

The counts from this question
Club	Bus	Walk	Total
A	2	4	6
B	3	5	8
Total	5	9	14

The counts from this question
Club	Bus	Walk	Total
A	3	4	7
B	6	5	11
Total	9	9	18

The counts from this question
Club	Bus	Walk	Total
A	4	2	6
B	3	6	9
Total	7	8	15

The counts from this question
Club	Bus	Walk	Total
A	5	3	8
B	2	4	6
Total	7	7	14

The counts from this question
Club	Bus	Walk	Total
A	3	5	8
B	4	6	10
Total	7	11	18

The counts from this question
Club	Bus	Walk	Total
A	4	5	9
B	7	6	13
Total	11	11	22

The counts from this question
Club	Bus	Walk	Total
A	5	3	8
B	4	7	11
Total	9	10	19

Open stage PSAT 3.4 in the student workspace →

STAGE PSAT 3.5 · 8 PRACTICE PROBLEMS · 4 NEW-CONTEXT APPLICATIONS

Samples, Population Estimates & Limits

Goal: Estimate population counts or totals from random sample statistics and explain why the estimate is not an exact census.

Before you begin: Read the problem carefully and use the linked foundation lessons when a term or operation is unfamiliar.

Make sense of the idea

A population is the complete group of interest. A sample is a subset. A random sample can help estimate a population proportion or mean, but it still has sampling variability.

Choose a method

Estimate a population count by sample proportion × population size. Estimate a population total by sample mean × population size. Keep units consistent.

Check and interpret

A larger random sample usually gives a more stable estimate, but size alone does not repair a biased selection method. A survey only of volunteers at a sports club need not represent the whole school.

WORKED EXAMPLE 1

A researcher randomly samples 50 of 1100 residents; 12 use an audiobook service. Use the sample proportion to estimate the number of users in the population.

The sample proportion is $\displaystyle \frac{12}{50}$ .
The estimated count is $\displaystyle \left(\frac{12}{50}\right) \times 1100 = 264$ . This is an estimate, not a census.

264

WORKED EXAMPLE 2

A school report estimates $\displaystyle 23\%$ of a population prefers option A, using a random sample rather than a census. Must EXACTLY $\displaystyle 23\%$ of the population prefer A? Enter 1 for yes or 0 for no.

The $\displaystyle 23\%$ figure is a sample-based estimate.
Sampling variability means the population proportion need not equal it exactly. Enter 0.

Common pitfalls

Possible mix-up: An estimated count is the exact count.

Random sampling still varies; only measuring the full population gives a census count.

Possible mix-up: A large biased sample must be representative.

Who is selected matters as well as how many.

Explain it to yourself

In samples, population estimates & limits, what information determines your method, and how can you check whether your result fits the original conditions?

Preview the eight practice prompts

Problem 1
A researcher randomly samples 50 of 1000 residents; 10 use an audiobook service. Use the sample proportion to estimate the number of users in the population.
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Problem 2
A random sample has mean mass 8 grams. There are 120 parcels in the population. Estimate the total mass in grams.
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Problem 3
For a schoolwide estimate, 30 volunteers from a sports club are surveyed. Does this method give a random sample of the WHOLE school? Enter 1 for yes or 0 for no.
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Problem 4
A sample report estimates $\displaystyle 20\%$ of a population prefers option A, using a random sample rather than a census. Must EXACTLY $\displaystyle 20\%$ of the population prefer A? Enter 1 for yes or 0 for no.
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Problem 5New context
A town library randomly samples 50 of 1050 residents; 11 use an audiobook service. Use the sample proportion to estimate the number of users in the population.
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Problem 6New context
A random sample of parcels has mean mass 9 grams. There are 130 parcels in the population. Estimate the total mass in grams.
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Problem 7New context
To estimate schoolwide exercise habits, 31 volunteers from a sports club are surveyed. Does this method give a random sample of the WHOLE school? Enter 1 for yes or 0 for no.
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Problem 8New context
A school report estimates $\displaystyle 21\%$ of a population prefers option A, using a random sample rather than a census. Must EXACTLY $\displaystyle 21\%$ of the population prefer A? Enter 1 for yes or 0 for no.
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Open stage PSAT 3.5 in the student workspace →

STAGE PSAT 3.6 · 8 PRACTICE PROBLEMS · 4 NEW-CONTEXT APPLICATIONS

Rates, Units & Percent Changes

Goal: Track units in rates, square or cube length-conversion factors, and distinguish relative percent from percentage points.

Before you begin: Read the problem carefully and use the linked foundation lessons when a term or operation is unfamiliar.

Make sense of the idea

A conversion factor equals one in different units. Multiply so unwanted units cancel. A length conversion factor must be squared for area and cubed for volume.

Choose a method

A percent change is measured relative to a base: new = old × (1 ± rate). To recover the old amount, divide the new amount by the factor.

Check and interpret

Percentage points subtract two percentages directly. Relative percent change divides that difference by the old percentage. Successive percent changes multiply their factors.

WORKED EXAMPLE 1

Convert $\displaystyle 4\, m^{2}$ to cm². Enter only the number.

$\displaystyle 1\, m^{2} = 100^{2}$ cm² = 10,000 cm².
$\displaystyle 4\, m^{2} = 40000$ cm².

40000

WORKED EXAMPLE 2

A survey approval rate rises from $\displaystyle 23\%$ to $\displaystyle 33\%$ . What is the increase in PERCENTAGE POINTS?

$\displaystyle 33 - 23 = 10$ percentage points.
The relative percent increase would instead be $\displaystyle \left(\frac{10}{23}\right) \times 100\%$ , which is a different question.

Common pitfalls

Possible mix-up: One square meter is 100 square centimeters.

Each side contributes a factor of 100; it is 10,000 cm².

Possible mix-up: Increasing then decreasing by the same percent restores the original.

The second change uses a different base. Multiply both factors.

Explain it to yourself

In rates, units & percent changes, what information determines your method, and how can you check whether your result fits the original conditions?

Preview the eight practice prompts

Problem 1
Convert $\displaystyle 2\, m^{2}$ to cm². Enter only the number.
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Problem 2
Convert 2 cm³ to mm³. Enter only the number.
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Problem 3
An item costs $80 after $\displaystyle a\, 20\%$ discount. What was its original price in dollars?
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Problem 4
A percentage rises from $\displaystyle 20\%$ to $\displaystyle 30\%$ . What is the increase in PERCENTAGE POINTS?
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Problem 5New context
A garden covers $\displaystyle 3\, m^{2}$ . How many square centimeters is that?
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Problem 6New context
A container holds 3 cm³. How many cubic millimeters is that?
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Problem 7New context
A jacket costs $88 after $\displaystyle a\, 20\%$ discount. What was its original price in dollars?
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Problem 8New context
A survey approval rate rises from $\displaystyle 21\%$ to $\displaystyle 31\%$ . What is the increase in PERCENTAGE POINTS?
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Open stage PSAT 3.6 in the student workspace →

Browse another level →

Data Analysis: Evidence & Predictions

Standard Deviation, Center & Outliers

Move the dots. Watch the spread.

Make sense of the idea

Choose a method

Check and interpret

Compare A:6\displaystyle A : 6A:6, 7, 8; B:4\displaystyle B : 4B:4, 7, 10. Which has greater standard deviation? Enter 1 for A, 2 for B, or 3 if equal.

Five commute times are 6, 7, 8, 9, 10. Only the largest value is replaced by 56. What is the new median?

Common pitfalls

Explain it to yourself

Dot Plots, Histograms & Frequency Tables

Same observations, different displays

Make sense of the idea

Choose a method

Check and interpret

A frequency table lists score 4:2\displaystyle 4 : 24:2 observations; score 5:3\displaystyle 5 : 35:3 observations; score 6:1\displaystyle 6 : 16:1 observation. What is the mean score?

A delivery-time histogram contains 8 values in [0,10), 10 in [10,20), and 1 in [20,30). Can the EXACT mean be determined from these counts alone? Enter 1 for yes or 0 for no.

Common pitfalls

Explain it to yourself

Scatterplots & Lines of Best Fit

A fitted line follows the pattern

Make sense of the idea

Choose a method

Check and interpret

A fitted line is y=4 x+7\displaystyle y = 4\, x + 7y=4x+7. What y-value does it predict at x=4\displaystyle x = 4x=4?

A scatterplot model was built using x-values from 6 to 16. Predicting at x=26\displaystyle x = 26x=26 is which type? Enter 1 for interpolation or 2 for extrapolation.

Common pitfalls

Explain it to yourself

Two-Way Tables & Conditional Probability

First choose who can be selected

Make sense of the idea

Choose a method

Check and interpret

A two-way table gives club A: bus 4, walk 6; club B: bus 5, walk 7. Given a student is in club A, what is the probability they take the bus? Enter a fraction.

A transport survey gives club A: bus 8, walk 6; club B: bus 5, walk 7. Given that a student takes the bus, what is the probability they are in club A?

Common pitfalls

Explain it to yourself

Samples, Population Estimates & Limits

Make sense of the idea

Choose a method

Check and interpret

A researcher randomly samples 50 of 1100 residents; 12 use an audiobook service. Use the sample proportion to estimate the number of users in the population.

A school report estimates 23%\displaystyle 23\%23% of a population prefers option A, using a random sample rather than a census. Must EXACTLY 23%\displaystyle 23\%23% of the population prefer A? Enter 1 for yes or 0 for no.

Common pitfalls

Explain it to yourself

Rates, Units & Percent Changes

Make sense of the idea

Choose a method

Check and interpret

Convert 4 m2\displaystyle 4\, m^{2}4m2 to cm². Enter only the number.

A survey approval rate rises from 23%\displaystyle 23\%23% to 33%\displaystyle 33\%33%. What is the increase in PERCENTAGE POINTS?

Common pitfalls

Explain it to yourself

Compare $\displaystyle A : 6$ , 7, 8; $\displaystyle B : 4$ , 7, 10. Which has greater standard deviation? Enter 1 for A, 2 for B, or 3 if equal.

A frequency table lists score $\displaystyle 4 : 2$ observations; score $\displaystyle 5 : 3$ observations; score $\displaystyle 6 : 1$ observation. What is the mean score?

A fitted line is $\displaystyle y = 4\, x + 7$ . What y-value does it predict at $\displaystyle x = 4$ ?

A scatterplot model was built using x-values from 6 to 16. Predicting at $\displaystyle x = 26$ is which type? Enter 1 for interpolation or 2 for extrapolation.

A school report estimates $\displaystyle 23\%$ of a population prefers option A, using a random sample rather than a census. Must EXACTLY $\displaystyle 23\%$ of the population prefer A? Enter 1 for yes or 0 for no.

Convert $\displaystyle 4\, m^{2}$ to cm². Enter only the number.

A survey approval rate rises from $\displaystyle 23\%$ to $\displaystyle 33\%$ . What is the increase in PERCENTAGE POINTS?