Statistics chapter 3

what is an average?

a single value that represents centre of data set

measure of central tendency

how do you find the median position for a frequency table?

1/2 (n+1)

how do you calculate the estimated median by linear interpolation?

L + ((n/2 − F) ÷ f) × w

L = lower boundary of the median class

n = total frequency

F = cumulative frequency before the median class

f = frequency of the median class

w = width of the median class.

what is the assumption behind interpolation?

the data is spread evenly across the class

how to calculate frequency density?

frequency / class width

what is the geometric mean?

ⁿ√(x₁ × x₂ × … × xₙ)

when do you use a geometric mean?

For average percentage change

what is the equation for weighted mean?

Σ(value × weight) ÷ Σweights = Σwx ÷ Σw

when do you use a weighted mean?

When values have different importance or group sizes

what does dispersion measure?

how spread out the data is

which graph do you use for a discrete cumulative frequency?

a step polygon

what is standard deviation?

a measure of how far all the values deviate from the mean

bigger SD = more spread out

A- minimum value

B- Q1

C- Q2

D- Q3

E- maximum value

F- median

G- whiskers

what type of skew is this?

positive skew

what type of skew is this?

no skew

what type of skew is this?

negative skew

what does mean > median > mode indicate?

positive skew

what does mode > median > mode indicate?

negative skew

what are the pros and cons of using mean?

Uses all data, and needed for SD and skew

affected by extreme values + distorted by open-ended classes.

what are the pros and cons of using median?

Not affected by extreme values

easy to find

doesn’t use all the data values.

what are pros and cons of mode?

Easy to find

always a real data value

only average for qualitative data

may be no mode or more than one.

which is the best average if there are outliers or skew?

the median

when is the mean the best choice?

When the data is roughly symmetrical with no extreme values

when you also need SD or skew.

which spread goes with which average?

mode with range

median with IQR

mean with SD