Measures of relative standing – zscore, quartiles, percentiles  Measures of Dispersion
Measures of relative standing – zscore, quartiles, percentiles
Lessons
Notes:
$\cdot$ $z_x$: zscore, a measure of how many standard deviations a data item $x$ is from the mean.
population: $z_x= \frac{x \mu}{\sigma}$
sample: $z_x= \frac{x \overline{x}}{s}$
zscore allows comparison of the variation in different populations/samples.
$\cdot$ Quartiles: values that divide the data set into quarters.
$Q_1=$ bottom 25% of data
$Q_2=$ Median $=$ bottom 50% of data
$Q_3=$ bottom 75% of data
$\cdot$ InterQuartile Range (IQR): represents the middle 50% of the data set.
$IQR= Q_3Q_1$
$\cdot$ Percentiles: indicates what percentage of the data falls below a certain value
$Percentile\;of\;X= \frac{number\;of\;data\;points\;less\;than\;X}{total\;number\;of\;data\;points}$
$\cdot$ Outliers: an outlier is a data point which lies an abnormal distance from all other data points.
Outliers are either,
a) above $Q_3+1.5(IQR)$ or b) below $Q_1 1.5(IQR)$

1.

2.
Determining the Quartiles
Find the quartiles for each data set: 
3.
Interquartile Range & BoxandWhisker Plot
For the data set: {8, 2, 20, 4, 9, 5, 6, 12, 10, 1} 
4.
Determining the Percentile
Sidney is taking a biology course in university. She got a mark of 78% and the list of all marks from her class (including her mark) is given by {56, 83, 74, 67, 47, 54, 82, 78, 86, 90}.