Statistics (Brilliant)

Question 1

Mathematical definition of mean

Answer 1

Sum of the set divided by the number of elements in the set

Question 2

Definition of median

Answer 2

Middle element of a set, with equal number of elements above and below

Question 3

How is the median determined if the cardinality of the set is even?

Answer 3

Mean of the middle two elements

Question 4

What is necessary regarding the arrangement of elements in a set in order to determine the median?

Answer 4

The data must be sorted

Question 5

Definition of mode

Answer 5

The value that appears most

Question 6

Can a set have more than one mode?

Answer 6

Yes

Question 7

What advantages does mode have over other measures of centrality?

Answer 7

It can evaluate non-numerical data and it can identify lurking variables in bimodal distributions

Question 8

What disadvantage does mode have over other measures of centrality?

Answer 8

It’s the least useful for inferring about the rest of the data

Question 9

What advantage does median have over mean?

Answer 9

It’s less affected by outliers

Question 10

How are the 1st, 2nd, and 3rd quartiles defined?

Answer 10

1st quartile is the median of the lower half of the data with 25% of data points before it; 2nd quartile is the median; 3rd quartile is the median of the upper half of the data with 25% of the data points above it

Question 11

What is the interquartile range?

Answer 11

The difference between the 1st and 3rd quartiles

Question 12

What is the definition of an outlier?

Answer 12

Less than the 1st quartile - 1.5 x interquartile range, or greater than the 3rd quartile + 1.5 x interquartile range

Question 13

Definition of expected value

Answer 13

Sum of (value x probability) for all values in set

Question 14

Definition of complement

Answer 14

All of the events that aren’t the event in question

Question 15

Sum rule #1 (for mutually exclusive events): P(AvB) = ?

Answer 15

P(AvB) = P(A) + P(B)

Question 16

Sum rule #2 (for non mutually exclusive events): P(AvB) = ?

Answer 16

P(AvB) = P(A) + P(B) - P(A&B)

Question 17

Product rule: P(A&B) = ?

Answer 17

P(A&B) = P(A) x P(B)

Question 18

What is Simpson’s Paradox?

Answer 18

A reversal of outcomes between individual cases and the overall total.

Question 19

What is the definition and range of the correlation coefficient r?

Answer 19

-1 <= r <= 1, representing the strength and direction of a linear relationship

Question 20

What is a residual?

Answer 20

Difference between actual y-value and predicted y-value

Question 21

What is the residual sum of squares (SSR)?

Answer 21

Sum of the squares of the residuals

Question 22

What is the total sum of squares (SST)?

Answer 22

Sum of the squares of the residuals relative to the mean value of y

Question 23

What is the coefficient of determination (R²)

Answer 23

1 - (SSR/SST)

Question 24

What is a linear regression?

Answer 24

The line that minimizes the coefficient of determination

Question 25

What is regression to the mean?

Answer 25

If a variable is measured at an extreme value, the next measurement will likely be closer to the mean.

Question 26

What is Kelley’s formula for estimated ability?

Answer 26

Estimated ability = (reliability)(score) + (1 - reliability)(average group score)

Question 27

Which show more variation, smaller or larger data sets?

Answer 27

Smaller