measures of dispersion

stats that tell you hoe clustered or spread out your data is around its mean

what are the mean, the median, and the mode not able to do?

• doesnt allow us to describe the differences between groups inside the dataset

  • dont allow us to see the activity of the data points

what do the measures of dispersion include? (4 things)

1. range

2. interquartile range

3. variance

4. standard deviation

what is range?

• take largest value (the maximum)

• subratct the smallest value (the minimum)

what does the range tell us?

• how distant your smallest and largest values are

  • especially when the mean, medians, and modes are almost the same

cons of knowing the range

• only takes into account the 2 most extreme points of the data

• needs other measurese of dispersion to get the bigger picture

what are quartiles?

• results of diving yout data into "quarters”

• median cuts the data in half, the quartiles cut the data in 4

what is the first quartile (Q1)?

• data point half way betwwen your lowest value and the median

• first 25% of the data

what is Q2?

• the median

what is Q3?

• aka upper quartile or third quartile

• data point half way between the median and the highest value

• 25% of the data is above it

what is Q0?

• the minimum

what is Q4?

• the maximum

what is the five number summary?

• set of descriptive stats

  1. minimum

  2. q1

  3. q2

  4. q3

  5. maximum

what is interquartile range?

• difference between Q3 value and Q1 value

what does the interquartile range tell us?

• the range within which the middle 50% of your data falls

what is the advantage of knowing the interquartile range?

• generally givers a clearer idea of the dispersion of data

  • it is not sensitive to extreme values

what are Box plots? (aka whisker plots/candlestick chart)

• graphical display of the 5 number summary (min, q1, q2, q3, max)

con of box plots

• dont give much detail about the data’s distributions

what are box plots useful for?

• detecting whether or not your distribution has

  • outliers

  • or is skewed

• comparing the distribution of different data points or subgroups

  • center, spread, and range are clearly displayed

Box plot

what are outliers?

• datapoints that are an abnormal distance above or below the other data in your sample

how to find outliers?

• with the interquartile range (IQR)

  • multiple the IQR by 1.5

    • mild outlier: if the value is less than Q1 - 1.5(IQR) or greater than Q3 + 1.5(IQR)

    • extreme outliers: more than 3IQR above Q3 or 3IQR below Q1

what are the types of outliers?

• multiple the IQR by 1.5

  • mild outlier: if the value is less than Q1 - 1.5(IQR) or greater than Q3 + 1.5(IQR)

  • extreme outliers: more than 3IQR above Q3 or 3IQR below Q1

what is the lower inner fence?

• voundary separating the low mild outliers

what is the upper inner fence?

• boundary separating the high mild outliers

what are upper and lower outer fences?

• boundaries diving the extreme outliers from the rest of the data

what is variance?

• a measure of dispersion that captures how spread out all of the datapoints are in your data set

• describes the spread of our data in relation to the mean

how do you calculare variance”

• the average of the squared differences between each data point and the sample mean

what is standard deviation?

• square root of the variance

most frequently used measures of dispersion?

• variance

• standard deviation

what are the steps to calculate the variance?

• (value 1 - mean)² = “squared difference”

• add all squared differences and divide by the number of datapoints

  • - 1 (if your data is from a random big sample)

how to calculate variance using google sheets?

• =VARA for varianve of a sample

• =VARP for variance of population

what is standard deviation useful for?

• for comparing the dispersion of 2 variables (or categories of a variable) that have similar means

standard deviations are, like the mean, sensitive to _____.

outliers

what is the difference between the variance and the standard deviation?

• the standard deviation is the average distance from the mean

• the variance is the squared average distance from the mean

why is it better to interpret data using standard deviation (and not the variance)?

• because the standard deviation is always in the same unit of analysis as your dataset

  • centimeters, scores, height, goals, etc.