Chapter 2: Measures of Location and Spread, standard deviation

mean notation

x̄

sum of x values notation

Σx

notation for calculating the mean

x̄ = Σx/n

notation for calculating the mean from a frequency table

x̄ = Σfx/Σf

benefits of the median over mean

• unaffected by extreme values

notation to calculate the median for listed data (and rules)

n/2

• decimal = round up

• whole = halfway between this and the next

notation to calculate the median for grouped data (and rules)

n/2

• linear interpolation

formula to do linear interpolation for the median

start interval + ((fraction into class division/total frequency for class division) x class width)

what to do when there are gaps between intervals

round down/up to take lower and upper bounds

how to find the quartiles for listed data

• ignore median

• middle of lower and upper half

formula to find the LQ and UQ (and rules) for listed data

1/4n, 3/4n

• decimal = round up

• whole = halfway this one and next

formula to find the LQ and UQ for grouped data (and rules)

1/4n, 3/4n

• linear interpolation

formula to calculate the percentile

n x percentile/100

LQ notation

Q₁

Median notation

Q₂

UQ notation

Q₃

notation xth percentile

P_x

what is the 10th percentile equivalent to?

1st decile (D₁)

what are the measures of spread? (2)

• IQ range

• interpercentile range

What is deviation?

The distance of a data point from the mean

Standard deviation formula

What does variance mean?

Average squared distance from the mean

Standard deviation symbol

σ

What does a lower standard deviation mean for the data points?

More consistent because they are closer to the mean

What to change for standard deviation of grouped data?

Use the frequencies to multiply by the midpoints accordingly.

coding - if you square values, what happens to the mean?

not squared

measures of position and averages what happens if coded by + or -?

as per operation

measures of position and averages what happens if coded by x or ÷?

as per operation

measures of spread what happens if coded by + or -?

unaffected

measures of spread what happens if coded by x or ÷?

as per operation

how would the standard deviation be coded by y = 3x + 12?

only multiplied by 3