measures of location and spread

what is a measure of location?

a single value which describes a position in a data set

what is the measure of central tendency?

a measure of location that describes the centre of the data

what are the measures of central tendency?

averages

• mean

• median

• mode

if the measure of location describes a single value in the centre of the data, what is it called?

the measure of central tendency

what is the mode / modal class?

the value / class that occurs most often

what is the median?

the middle value when the data values are put in order?

how do you calculate the mean?

here

how do you calculate the mean for values in a frequency table?

here

x̄ = ?

Σx = ?

n = ?

x̄ = mean

Σx = sum of the data values

n = number of data values

how do you calculate the mean for values in a frequency table?

here

Σxf = ?

Σf = ?

Σxf = sum of the products of the data values and their frequencies

Σf = sum of the frequencies

which measures of central tendency are used for quantitative data?

• mode

• median

• mean

which measures of central tendency are used for qualitive data?

• mode

which data type can the mode be used to measure?

quantitative and qualitive

which data type can the median be used to measure?

quantitative

which data type can the mean be used to measure?

quantitative

when should the mode be used?

• quantitative or qualitive data

• data has 1 or 2 modes (bimodal)

when shouldn’t the mode be used?

when each data value occurs only once

when should the median be used?

• quantitative data

• used when there are extreme values, as they don’t affect it

which measure of central tendency should you use when there are extreme values?

the mode, since they don’t affect it

why should the mode be used when there are extreme values?

because the extreme values don’t affect the mode

when should the mean be used?

• quantitative data

• when a true measure of data, including all pieces of data, is needed

what is good about the mean?

it uses all pieces of data, therefore giving a true measure of the data

when shouldn’t you use the mean?

when there are extreme values, because it is affected by it

what does bimodal mean?

the data has 2 modes

which measures of central tendency are used for both quantitative and qualitive data?

• mode

if given the mean, how do you find the sum of data values?

sum of data values = mean x number of data values

what are the measures of location?

• measures of central tendency

  • mean

  • median

  • mode

• quartiles

• percentiles

what are quartiles?

the data split into quarters

• lower quartile = ¼ of the data

• median = ½

• upper quartile = ¾ of the data

Q₁ = ?

Q₂ = ?

Q₃ = ?

Q₁ = lower quartile, ¼

Q₂ = median, ½

Q₃ = upper quartile, ¾

what are percentiles?

a percentage of the data across. basically a quartile that isn’t confined to the 25%

what is the distance between each quartile?

25%

how do you find the lower quartile for discrete data?

n / 4 :

• whole number (a) - LQ is halfway between a and b, a.5

• not a whole number (a) - LQ is a

how do you find the upper quartile for discrete data?

n x ¾ :

• whole number (a) - LQ is halfway between a and b, a.5

• not a whole number (a) - LQ is a

how do you find the median for discrete data?

n / 2 :

• whole number (a) - LQ is halfway between a and b, a.5

• not a whole number (a) - LQ is a

how do you find the quartiles for grouped continuous data?

Q₁ = n/4 data value

Q₂ = n/2 data value

Q₃ = 3n/4 data value

how do you find quartiles and percentiles for grouped linear data?

linear interpolation

here

how do we use linear interpolation?

here

when using interpolation, what do we assume?

that the data values are evenly distributed within each class

what is on the top of a linear interpolation line?

i forgor

what is on the bottom of a linear interpolation line?

i forgor

more questions abt linear interpolation

what is a measure of spread?

a measure of how spread out the data is (duh)

what are the measures of spread?

• range

• interquartile range

• variance

what is the range?

the difference between the largest and smallest values in the data set

what is the interquartile range?

IQR = Q₃ - Q₂

what is good about the range?

it considers all the values in a data set

what is bad about the range?

it can be affected by extreme values

what is good about the IQR?

it is not affected by extreme values

what is bad about the IQR?

it only considers the spread of the middle 50% of data

what is the interpercentile range?

the difference between 2 given percentiles

how do we represent a percentile?

P₅₀ come back to this

what is the variance (σ²)?

the amount that each data point deviates from the mean by (x - x̄)

here

what is S_xx?

the summary statistic

here

what is the standard deviation (σ)?

the square root of the variance

here

what equation for variance is easier to use with raw data?

here

the mean of the squares - the square of the mean

what equation for variance is easier to use if you can find S_xx on your calculator?

here

what are the units for variance?

the units of the data squared

what is coding?

a way of simplifying statistical calculations by coding data values to make a new set of data values which are easier to work with

what is the formula for coding?

y = (x - a) / b

what is the mean of coded data?

y^- = (x^- - a) / b

what is the standard deviation of coded data?

σ_y = σ_x / b

• σ_y = standard deviation of coded data

• σ_x = standard deviation of original data

how do you find the mean of the original data given the statistics for the coded data?

x̄ = bȳ + a

how do you find the standard deviation of the original data given the statistics for the coded data?

σ_x = bσ_y