10th grade statistics and probability

Example

Survey: Likes science & is in Club — 19; Likes science & not in Club — 11; Doesn't like science & in Club — 5; neither — 12. Given a student is in the Club, what is the probability they like science? Simplest form.

1. Club members: 19 + 5 = 24
2. P = 19/24

Answer: 19/24

Example

Find the population standard deviation of: 8, 16

1. Mean = 12
2. Squared distances: 16, 16
3. σ = √(32 ÷ 2) = 4

Answer: 4

Example

In a histogram, a bar covers a class of width 5 and has frequency density 1.5. What is the frequency?

1. 1.5 × 5 = 7.5

Answer: 7.5

Example

A bag has 8 red and 7 blue counters. Two are taken out without replacement. Find P(both red) as a fraction in simplest form.

1. 8/15 × 7/14 = 56/210
2. = 4/15

Answer: 4/15

Example

P(A) = 0.5, P(B) = 0.5 and P(A and B) = 0.2. Find P(A or B).

1. 0.5 + 0.5 − 0.2 = 0.8

Answer: 0.8

Example

Set X: 34, 36, 38, 40, 42 Set Y: 22, 30, 38, 46, 54 Both have mean 38. Which set has the larger standard deviation?

1. Y

Answer: Y