Histogram & normal distribution

A histogram is a plot that lets you discover, and show, the underlying frequency distribution (shape) of a set of continuous data. This allows the inspection of the data for its underlying distribution (e.g., normal distribution), outliers, skewness, etc.

1. Histogram & Normal
distributionPractice
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2. Histogram
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A histogram is a plot that lets you discover, and show, the underlyingfrequency
distribution (shape) of a set of continuous data. This allows the inspection of
the data for its underlying distribution (e.g., normal distribution), outliers,
skewness,etc.
36, 25, 38, 46, 55, 68, 72, 55, 36, 38, 67, 45, 22, 48, 91, 46, 52, 61, 58,55

3. Let’s buildhistogram
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36,25,38,46,55,68,72,55,36,38,67,45,22,48,91,46,52,61,58,55

4. Approach tobins
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To construct a histogram from a continuous variable you first need to split the
data into intervals, called bins. In the example above, age has been split into
bins, with each bin representing a 10-year period starting at 20 years. Each bin
containsthenumberofoccurrencesofscoresinthedatasetthatarecontained
within that bin. For the above data set, the frequencies in each bin have been
tabulated along with the scores that contributed to the frequency in each bin
(seenext):

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6. Choosing the rightbins
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There is no right or wrong answer as to how wide a bin should be, but there are
rules of thumb. You need to make sure that the bins are not too small or too
large. Consider the histogram we produced earlier (see above): the following
histograms use the same data, but have either much smaller or largerbins

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8. BAR
Graph
ABarGraph (alsocalledBarChart)isagraphicaldisplayofdatausingbarsof
differentheights.

9. Bar graph
example
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10. Example
1
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11. Histogram vs Bargraph
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12. Normaldistribution
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14. Normal distribution -continued
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Many things closely follow a NormalDistribution:
●heights ofpeople
●size of things produced by machines
●errors inmeasurements
●blood pressure
●marks on atest

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16. The Standard Deviation is a measure of how spreadout
numbersare
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17. Empiricalrule
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18. Empirical rule -
1
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19. Empirical value -
2
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20. Practice problem1
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22. It is good to know the standard deviation, because we can say that anyvalue
is:
●likely to be within 1 standard deviation (68 out of 100 shouldbe)
●very likely to be within 2 standard deviations (95 out of 100 shouldbe)
●almost certainly within 3 standard deviations (997 out of 1000 shouldbe)
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23. Standardscores
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The number of standard deviations from the mean is also calledthe
"Standard Score", "sigma" or"z-score".
What is his Z-score?

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26. Practiceproblem
A survey of daily travel time had these results (in minutes): Convert firstthree
values into Z-scores (Assume Normaldistribuion)
26, 33, 65, 28, 34, 55, 25, 44, 50, 36, 26, 37, 43, 62, 35, 38, 45, 32,
28,34
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28. Graphically same data inZ-scores
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29. Formula forZ-score
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31. Reference
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https://www.mathsisfun.com/data/standard-normal-distribution.html