Exploring Data

2 ways to explore data

summarising

• tabular or numerically (descriptive statistics)

displaying

• graphically (boxplots, histograms, bar charts, scatterplots)

frequency table

describes data by showing the number of objects / events for each data category

contingency tables

two-way or multi-way frequency tables to summerise the relationship between 2 or more categorical variables

descriptive statistics includes

measures of central tendency

• mean, median, mode

measures of dispersion

• range, quartiles, variance, standard deviation

mean

average

x

adding all numbers in a set of values and dividing by total number of cases

median

middle value in an ordered set of values

useful to know when extreme values are present to find midpoint

mode

value that occurs most frequently

can have more than one mode in a dataset

no mode when all items occur the same number of times

range

the difference between the largest and smallest observations in the dataset

quartiles

three points that divide the data into 4 groups

Q1- lower quartile or 25th percentile

Q2 - sample median or 50th percentile

Q3- upper quartile or 75th percentile

interquartile range

IQR = Q3 - Q1

5-number summary

5 values (minimum, Q1, Q2, Q3, maximum) provide a numerical summary of a set of data called the 5 number summary

variance and SD

these related measures give the idea of variability by calculating the extent to which each observation deviates from the mean

SD calculation

the standard deviation is the square root of the variance and is most used when reporting results

how is variance calculated

the difference between each data point and the mean is calculated, but the average of all the deviations cannot be used since negative values will cancel out the positive ones

hence, the differences are squared, then summed up and divided by the number of cases to obtain the variance

variance

how spread out a set of numbers is from its average value (the mean)

small variance means data points are close to the mean

large variance means the numbers are spread far apart

SD

measures data variability around the mean of a sample of the population

SE

Indicates the indicates the precision of the estimated mean of a population

always smaller than the SD

boxplot

normal distribution

symmetrical around midpoint

bell shaped (histogram)

required for accurate stats representation

histogram

scatterplot

useful for examining relationship between 2 continuous variables

bar chart

used for categorical variables

height = size of group

scatterplot relationships

linear

strong (clustered points) or weak (scattered points)

positive (increase y and x axis) or negative