Statistics & probability

Question 1

Discrete data

Answer 1

Question 2

Continuous data

Answer 2

Question 3

What is the difference between discrete and continuous data?

Answer 3

Discrete data may take on exact values, while continuous data lies in a range.

Question 4

Types of sampling

Answer 4

• Simple
• Convenience
• Systematic
• Quota
• Stratified

Question 5

Simple sampling

Answer 5

• Achieving randomness by a simple, completely random process.
• You choose items out of a hat or you use a random number generator to pick items from a list.

Question 6

Convenience sampling

Answer 6

• Choosing a sample based on how easy it is to find the data.
• You ask the first twenty people who walk past you to answer your survey.

Question 7

Systematic sampling

Answer 7

• If data is listed, selecting a random starting point and then choosing the rest of the sample at a consistent interval in the list.
• You roll a die and get a 6, so you start with the 6th item and then choose every 10th item in the list after that.

Question 8

Quota sampling

Answer 8

• Choosing a sample that is only comprised of members of the population that fit certain characteristics.
• You want a sample of 50, but they must all be ladies between the ages of 16 and 25. The selection is not random, a convenience method can be used.

Question 9

Stratified sampling

Answer 9

• Choosing a random sample in a way that the proportion of certain characteristics matches the proportion of those characteristics in the population.
• The population is 45% male and 55% female, so you make a random sample of 100 people that has 45 men and 55 women in it.

Question 10

Nathanael decides to change his sampling strategy. He is now choosing randomly ten percent of the students from each class.

State the type of sampling Nathanael is using now.

Answer 10

• Stratified
• Because Nathanael is constructing his random sample in proportion to the size of each class, he is using stratified sampling.

Question 11

A discrete numerical variable takes an ___

Answer 11

Exact number value

Question 12

The higher the standard deviation or variance, the more ___

Answer 12

Spread out the data is

Question 13

The maths students in a school count their money and calculate the mean to be μ=€15. Everyone in the class agrees to donate €5 to a local charity.

Find the mean amount of money the students have now.

Answer 13

μ=€10

Since every student is donating €5, the money each one has is decreased by 5. Since they have subtracted 5 from all of the data, the mean will also decrease by 5.

Question 14

Equations used to find out if something is an outlier

Answer 14

If it falls outside of the range:

Q1 - 1.5 x IQR

or

Q3 + 1.5 x IQR

Question 15

Diagram showing Q1 and Q3 on a bell curve

Answer 15

Question 16

What do different r values mean?

Answer 16

0 -> 0.5 or 0 -> -0.5 = no correlation

0. 5 -> 0.75 or -0.5 -> -0.75 = weak correlation
1. 75 -> 1 or -0.75 -> -1 = strong correlation

Question 17

If a data set gets multiplied by 5, what happens to the mean, standard deviation, and variance?

Answer 17

Mean: gets multiplied by 5

Standard deviation: gets multiplied by 5

Variance: new standard deviation squared

Question 18

What happens to the mean and standard deviation if you add 5 to a data set?

Answer 18

Mean: increses by 5

Standard deviation: doesn’t change (spread is the same)

Question 19

Normal distribution curve with IQRs shown

Answer 19