A&A SL: Core Topics: Statistics

a form to more accurately represent the spread of data

the square root of the variance

measures the degree to which the data deviates from the mean

a non-resistant measure of spread

only useful if the data is symmetrical

if a sample from a large population the sample standard deviation (s) is a more accurate estimate

represents a more accurate spread of data

the average of the squares of the distances from the mean

If data values (xᵢ) are situated close around the mean (μ) then (xᵢ - μ)² would be too small and have too small of a variance

the values below which a certian percentage of the data lies

• Q1 is the 25th percentile

• Q2 is the 50th percentile

• Q3 is the 75th percentile

made of the cumulative frequency

a smooth graph with curves

shows the number/proportion of numbers that lie above or below a particular value

can create column for the cumulative frequency within a frequency table

will create a frequency graph which create a graph of smooth curves

a visual comparison of the distribution of two data sets

used to easily compare statistics such as the median, range, and IQR

extraordinary data separated from the main body of data

applies to any value larger or smaller than the boundaries

• upper boundary = upper quartile + 1.5 x IQR

• lower boundary = upper quartile + 1.5 x IQR

outliers are marked with an Astrid on a Wisker box plot

it is possible to have more than one outlier

made up of:

• the minimum value

• the lower quartile Q1

• the median Q2

• the upper quartile Q3

• the maximum value

will show the five number summary of the data set

rectangular box represents the “middle“ half

lower whisker shows the 25% smallest values

upper whisker shows the 25% largest values

shows the systematic distribution of a box plot

AKA: IQR

the median divides the ordered set into halves and then in half again by quartiles

IQR = Q3 - Q1

Lower Quartile (Q1)

• middle value of the lower half

Upper Quartile (Q3)

• middle value of the upper half

Interquartile range (IQR) (Q2)

• the range of the middle half of data

the difference between the maximum data value and the minimum data value

Range = maximum - minimum

not particularly reliable as it only uses two data values

easily influenced by extreme values and outliers

useful for choosing class intervals

calculated mean represents the approximated value

reason to why you need to know each individual data value

a result of assuming data values within classes

a representation of all data values in a class interval

helps to add the data values

found in a frequency table

used to easily find the mode

gives data a halfway point

only accounts for middle values

not affected by extreme values

commonly used and easy to understand

accounts for all values

affected by extreme values

gives the most usual value

only accounts for common values

unaffected by extreme values

when a data set has two values that occur most frequently

measured with the mean, median, and mode

most frequently occurring value in a discrete data set

the modal class in continuous data sets

if a data set has two values that both occur most frequently it is bimodal

if the data set has three or more most frequently occurring values the mode becomes inapplicable

middle value of an ordered data set

splits data in half

• EX: the median mark for a test is 73% then you know that half the class scored less than or equal to 73% and half the class scored greater than or equal to 73%

if there is an odd number of data values the median is one of the original values

if there is an even number of data values then the median will be the average of the two middle numbers

if there are n data values listed in order from smallest to largest the median is the (n+1/2)th data value

the statistical name for an arithmetic average

mean = the sum of all data values / the number of data values

use ˉx to represent the mean of a sample

use μ to represent the mean of a population

• you do not always have data from all the population members so the exact value of μ is unknown

• collect data from a sample of a population and use the mean of the sample ˉx as an approximation for μ