7th Math: Statistics & Probability practice questions and exam guide

Class A: mean = 85, MAD = 3. Class B: mean = 85, MAD = 9. Which statement is best supported?

1. Class A scores are more consistent than Class B
2. Class B has a higher average
3. Class A has more students
4. The two classes are identical

Answer: A — Class A scores are more consistent than Class B

Same mean, smaller MAD = tighter clustering. (B) means are equal; (C) MAD says nothing about count; (D) MADs differ.

You spin a spinner and record outcomes: A 30, B 10, C 10. The probability model is BEST described as:

1. Uniform with P = 1/3 for each
2. Non-uniform — P(A) ≈ 3/5, P(B) ≈ 1/5, P(C) ≈ 1/5
3. Theoretical 1/2 each
4. Impossible — counts don't sum to 100

Answer: B — Non-uniform — P(A) ≈ 3/5, P(B) ≈ 1/5, P(C) ≈ 1/5

Observed frequencies are uneven, so a non-uniform model fits: 30/50, 10/50, 10/50. (A) ignores data; (C) makes no sense; (D) counts sum to 50, fine.

Margin of error:

1. Allowable difference between sample estimate and true value
2. Random
3. Always 0
4. Has no meaning

Answer: A — Allowable difference between sample estimate and true value

A) Standard. B/C/D) Each is incorrect.

Random sampling is important because:

1. It is faster than other methods
2. It ensures every member of the population has an equal chance of being selected, reducing bias
3. It always gives a perfectly accurate result
4. It requires fewer calculations

Answer: B — It ensures every member of the population has an equal chance of being selected, reducing bias

Random sampling reduces selection bias by giving all members an equal chance. (A) speed is a benefit but not the reason it's important; (C) 'perfectly accurate' is too strong; (D) not necessarily true.

What does P(A|B) mean?

1. P(A) divided by P(B)
2. P(A) plus P(B)
3. Probability of A given that B has already occurred
4. P(A) multiplied by P(B)

Answer: C — Probability of A given that B has already occurred

P(A|B) is conditional probability — the probability of A occurring given B has occurred. (A) is related to Bayes' theorem but not the definition; (B) is union for mutually exclusive; (D) is P(A and B) for independent events.

A fair die is rolled 60 times. Expected number of times you'd roll a 4:

1. 4
2. 6
3. 10
4. 15

Answer: C — 10

Expected = probability × trials = (1/6) × 60 = 10. (A) the number on the die; (B) total / probability reversed; (D) divided by 4.

Convenience sample:

1. People easy to reach; can be biased
2. Random
3. Stratified
4. Census

Answer: A — People easy to reach; can be biased

A) Standard. B/C/D) Each is incorrect.

To compare typical scores of two classes when the data are skewed, the BEST single measure is:

1. Mean
2. Mode
3. Median
4. Range

Answer: C — Median

Skewed data have outliers that pull the mean. Median is robust to skew and best represents the typical value. (A) skewed by outliers; (B) may be unrepresentative; (D) measures spread, not center.

Which is the BIGGEST source of bias in 'an online poll on a soccer fan site asks visitors about the best sport'?

1. Sample size is small
2. The site self-selects soccer fans — answers won't represent the general public
3. The poll is too long
4. Online polls are always accurate

Answer: B — The site self-selects soccer fans — answers won't represent the general public

Self-selection by site visitors guarantees a skewed sample. (A) even a huge sample of soccer fans is still biased; (C) irrelevant; (D) false.

Which simulation BEST models choosing a random month of the year?

1. Flipping a coin
2. Rolling a 6-sided die
3. Spinning a 12-section spinner with equal sections
4. Drawing from a deck of cards

Answer: C — Spinning a 12-section spinner with equal sections

12 equal sections = 12 equal-probability outcomes, matching 12 months. (A) only 2 outcomes; (B) 6 outcomes; (D) 52 cards with unequal category sizes.

Use a random digit table (0-9) to simulate a 30% chance event. Which assignment works?

1. Digits 0, 1, 2 = event occurs (3 of 10 digits)
2. Only digit 3 = event occurs
3. Even digits = event occurs
4. Digits 0-6 = event occurs

Answer: A — Digits 0, 1, 2 = event occurs (3 of 10 digits)

3 of 10 digits = 30%. (B) 1/10 = 10%; (C) 5/10 = 50%; (D) 7/10 = 70%.

You survey 50 random students and find 30 have a pet. Best estimate for the fraction of all students with a pet:

1. 30
2. 0.3
3. 50
4. 0.6

Answer: D — 0.6

30/50 = 0.6 = 60%. This is the best estimate from the sample. (A) count, not fraction; (C) total surveyed; (B) fraction without a pet.

In a school of 800, you survey 50 random students. 30 like pizza. Estimate how many in the whole school like pizza.

480. (30/50 = 60%; 60% of 800 = 480.)

As you do MORE trials, what happens to experimental probability?

It tends to get closer to the theoretical probability. (Law of large numbers.)

Roll 2 dice. P(sum = 7)?

6/36 = 1/6. (Pairs: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1).)

P(heads on coin)?

1/2.

What are 'mutually exclusive' events?

Events that can't happen at the same time. Like rolling a 1 and rolling a 2 in one toss.

Roll 2 dice. P(sum = 12)?

1/36. (Only (6,6).)