A sample of 40 fish finds 8 tagged. The lake has 200 fish. About how many were tagged? — 40.8/40 = 20%. 200 × 0.20 = 40 fish estimated tagged.
To estimate the number of red marbles in a bag of 250, you draw 20 and find 5 are red. About how many are red in the whole bag? — 62.5.5/20 = 25%. 250 × 0.25 = 62.5 ≈ 63 marbles.
A city of 10,000 people surveys 100 randomly. 60% prefer option A. About how many in the city prefer option A? — 6,000.10,000 × 0.60 = 6,000 people.
Which sampling method would produce the MOST reliable inference? — Randomly select 50 students from the school roster.Randomly selecting from the school roster gives every student equal chance, producing the most reliable sample.
What does a larger random sample provide compared to a smaller one? — More reliable inferences with less error.Larger random samples produce more reliable inferences. Roughly, doubling the sample size halves the margin of error.
A random sample finds that 15 of 25 sixth-graders prefer pizza. Of 400 sixth-graders in the school, about how many prefer pizza? — 240.15/25 = 60%. 400 × 0.60 = 240.
You want to estimate the average height of students in your school. Which sample is MOST appropriate? — A randomly selected group of 30 students.A randomly selected group avoids bias from choosing a non-representative group (e.g., tall basketball players).
From a sample of 50 households, 35 own a dog. In a neighborhood of 300 households, about how many own a dog? — 210.35/50 = 70%. 300 × 0.70 = 210.
A school of 500 students is split equally between 7th and 8th graders. You want both grades represented proportionally in your sample of 50. How many 7th graders should be in the sample? — 25.Equal split = 50% each. 50 × 0.50 = 25 students from each grade.
A sample of 20 cars on a highway finds 4 with expired tags. There are 1,000 cars on the highway. Estimate the number with expired tags. — 200.4/20 = 20%. 1,000 × 0.20 = 200 cars.
What is the purpose of making an inference from a sample? — To draw conclusions about the population using the sample data.The purpose of statistical inference is to draw conclusions about the population based on what was observed in the sample.
Data set A: 10, 10, 20, 30, 30. Data set B: 18, 19, 20, 21, 22. Both have mean 20. Which has greater spread? — Data set A.Data set A spans from 10 to 30 (range 20); Data set B spans 18–22 (range 4). A has much greater spread.
Team A: mean 85, MAD 3. Team B: mean 85, MAD 10. Which team is more consistent? — Team A, smaller MAD means less variability.MAD measures average distance from the mean. A smaller MAD means data is clustered tighter — Team A is more consistent.
When should you use median instead of mean to compare data? — When the data has outliers or is skewed.The median is resistant to outliers. When extreme values are present, the median better represents the "typical" value.
Class A: median 75, IQR 8. Class B: median 75, IQR 20. What can you infer? — Class A is more consistent (smaller IQR).IQR measures spread of the middle 50%. Class A's IQR of 8 indicates middle-range scores are more clustered.
Data: 5, 5, 5, 5, 5. What is the MAD? — 0.Mean = 5. Each value's distance from mean = 0. MAD = 0. Zero variability means perfect consistency.
To describe how "spread out" data is, which measure should you report? — IQR or MAD.The IQR and MAD are measures of spread/variability. Mean and median describe the center, not the spread.
Two data sets have the same median but different IQRs. The one with the larger IQR has: — More spread in the middle 50%.Larger IQR means the middle 50% of the data (from Q1 to Q3) is more spread out.
What does it mean to "compare distributions"? — Analyzing and contrasting the center AND spread of two data sets.Comparing distributions means analyzing BOTH center (mean or median) AND spread (range, IQR, or MAD) of two data sets.
In a box plot, the box spans from Q1 to Q3. What does the length of the box represent? — The IQR.The box in a box plot spans from Q1 to Q3. Its length is the IQR (Interquartile Range).
The mean of five numbers is 20. Four of them are 10, 15, 25, and 30. What is the fifth number? — Total must be 100; 10+15+25+30=80; fifth = 20.Sum = mean × count = 20 × 5 = 100. Known sum = 10+15+25+30 = 80. Fifth = 100−80 = 20.
A bag has 4 red, 3 blue, and 5 green marbles. What is P(green)? — 5/12.Total = 4+3+5 = 12. P(green) = 5/12.
What is the complement of an event with probability 3/8? — 5/8.P(complement) = 1 − P(event) = 1 − 3/8 = 5/8.
You flip a coin and roll a die. What is the total number of possible outcomes? — 12.Outcomes = 2 × 6 = 12. The sample space has 12 equally likely outcomes.
If P(A) = 1/4 and P(B) = 1/3, and A and B are independent, what is P(A and B)? — 1/12.P(A and B) = P(A) × P(B) = (1/4)(1/3) = 1/12.
A bag has 3 red, 2 blue, and 5 green marbles. What is P(NOT green)? — 7/12.P(not green) = 1 − P(green) = 1 − 5/12 = 7/12.
You roll two dice. What is the probability that both show a 6? — 1/36.P(6 on die 1) × P(6 on die 2) = (1/6)(1/6) = 1/36.
How many outcomes are in the sample space when you flip 3 coins? — 8.2 × 2 × 2 = 8. Each coin has 2 outcomes, and you multiply for independent events.
A standard deck has 52 cards. What is P(drawing an ace)? — Both 1/13 and 4/52 are equivalent.P(ace) = 4/52 = 1/13. Both forms are correct.
Two events are independent if: — The outcome of one does not affect the other.Independent events: the occurrence of one event does not change the probability of the other.
A spinner has 8 equal sections numbered 1–8. What is P(prime number)? — 1/2.Prime numbers 1–8: 2, 3, 5, 7 — that's 4 primes. P = 4/8 = 1/2.
You draw a card from a deck (52 cards, 4 suits, 13 per suit). What is P(heart or spade)? — 1/2.Hearts = 13, Spades = 13. Total = 26. P(heart or spade) = 26/52 = 1/2.