2.3 ONE QUANTITATIVE VARIABLE: USING PERCENTILES

How can we visualize quantitative data?

• Dotplot

• Histograms

• Boxplot (or Box-and-whisker plot)

What is the general shape of the data?

• Symmetric,

• Left- or Right-Skewed,

• Bell-Shaped,

• Uniform

Where are the data values centered?

– Mean

– Median

How do the data vary?

– Maximum and minimum

– Range

– Standard deviation

– 95% Rule for bell-shaped data

– Chebyshev’s Rule for data not necessarily bell-shaped

– Five Number Summary

what is Chebyshev’s Rule for data?

states that for any data set, regardless of its shape, the proportion of observations lying within k standard deviations of the mean is at least 1 - 1/k² and K>1

what is the 5 number summary?

min, q1 (25%), med, q3 (75%), max

What is the position of a data value relative to the data set?

– z-score

– Percentile

– Quartile

– Median

– IQR

 Are there unusual values and how do we identify them?

 Outlier (IQR Method)

what is Percentile?

The Pth percentile is the value which is greater than P% of the data.

what is median?

(m)=50th percentile=the value that splits the data in half

• The median is the middle entry if an ordered list of the data values contains an odd number of entries.

  • The median is the average of the middle two values if an ordered list contains an even number of entries.

what percentile is q1?

25%

what percentile is q3?

75%