Distributions and Calculations

Question 1

Distribution

Answer 1

List or function showing all the possible values/intervals of the data and how often they occur

Question 2

Four Main Distributions

Answer 2

Positive - Tail heads towards positive

Negative - tail heads towards negative

Binomial - two distinct peaks

Symmetric - tails are equal

Question 3

Leptokurtic (L)

Answer 3

Long tails relative to normal distribution

Question 4

Platykurtic

Answer 4

Short tails relative to normal distribution

Question 5

Class (Class Intervals)

Answer 5

Division of data into Bin Widths

Question 6

Class Frequency

Answer 6

Number of observations within a class of data

Question 7

Bin Width Rules

Answer 7

Surges = 1 + Log2(N)

Rice = 2 x Cubed Root N

N = Total number of observations

Question 8

Balance Scale

Answer 8

Point at which distribution is even

Question 9

Center Distribution Using Smallest Absolute Deviation

Answer 9

Absolute Deviation = Sum of the difference in values from deviation

Center Distribution Using Smallest Absolute Deviation = smallest number for which the sum of absolute deviation is smallest

*Use median (midpoint)

Question 10

Center Distribution Using Smallest Squared Deviation

Answer 10

Squared Deviation = difference in values from deviation, squared

Center Distribution Using Smallest Squared Deviation = smallest number for which the sum of squared deviation is smallest

Question 11

Three Ways to Define a Central Tendency

Answer 11

1. Point at which distribution is balanced
2. Number which minimizes the sum of the absolute differences
3. Number which minimizes the sum of the squared differences

Question 12

Mode

Answer 12

Most frequently occurring value

Question 13

Median

Answer 13

Midpoint of a distribution ranked from lowest to highest

Median - medians are in the middle - middle number

*Use the median to calculate absolute deviations

Question 14

Mean

Answer 14

Total Value / Total Numbers = Mean (average)

• The mean is where we hope a distribution is balanced b/c it is the average
• Use the mean to calculate squared deviations

Question 15

Range

Answer 15

Highest Value - Lowest Value

Question 16

Interquartile Range (IRQ)

Answer 16

IRQ = 75th percentile - 25th percentile

IRQ = range of the middle 50% of the values

Question 17

Semi-Interquartile Range

Answer 17

IRQ / 2

Median + - the SIRQ = 50% of the values

Question 18

Variance

Answer 18

The expectation of the squared deviation of a random variable from its mean.

Measures how far a set of numbers are spread out from their average value

Question 19

Standard Deviation

Answer 19

Square root of the variance

Variance - average squared difference of the values from the mean