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$\cdot$ **$z_x$: z-score**, a measure of how many *standard deviations* a data item $x$ is from the *mean*.

population: $z_x= \frac{x- \mu}{\sigma}$

sample: $z_x= \frac{x- \overline{x}}{s}$

**z-score** 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.

$IQR= Q_3-Q_1$

$\cdot$ 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 $Q_1- 1.5(IQR)$

population: $z_x= \frac{x- \mu}{\sigma}$

sample: $z_x= \frac{x- \overline{x}}{s}$

$\cdot$ Quartiles: values that divide the data set into

$Q_1=$ bottom 25% of data

$Q_2=$

$Q_3=$ bottom 75% of data

$\cdot$ InterQuartile Range (IQR): represents the middle 50% of the data set.

$IQR= Q_3-Q_1$

$\cdot$ 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

Outliers are either,

a) above $Q_3+1.5(IQR)$ or b) below $Q_1- 1.5(IQR)$

- 1.a)Z-Scoreb)Quartilesc)InterQuartile Ranged)Percentiles
- 2.
**Using Z-score to Compare the Variation in Different Populations**

Charlie got a mark of 85 on a math test which had a mean of 75 and a standard deviation of 5. Daisy got a mark of 75 on an English test which had a mean of 69 and a standard deviation of 2. Relative to their respective mean and standard deviation, who got the better grade? - 3.
**Determining the Quartiles**

Find the quartiles for each data set:a){9, 3, 7, 5, 2, 8, 12}b){2, 3, 5, 7, 8, 9, 12, 15}c){2, 3, 5, 7, 8, 9, 12, 15, 35} - 4.
**Interquartile Range & Box-and-Whisker Plot**

For the data set: {8, 2, 20, 4, 9, 5, 6, 12, 10, 1}a)Determine the quartiles.b)Find the interquartile range.c)Construct a box-and-whisker plot.d)Which data points, if any, are outliers? - 5.
**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}.a)What percentile did she score in?b)Sidney’s friend Billy knows he got in the 70% percentile, what was his mark?

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