Editing Histogram (section)

==Examples==

This is the data for the histogram to the right, using 500 items:

[[File:Example histogram.png|thumbnail]]
{| class="wikitable" style="text-align:right"
!Bin/Interval!!Count/Frequency
|-
| −3.5 to −2.51 || 9
|-
| −2.5 to −1.51 || 32
|-
| −1.5 to −0.51 || 109
|-
| −0.5 to 0.49 || 180
|-
|  0.5 to 1.49 || 132
|-
|  1.5 to 2.49 || 34
|-
|  2.5 to 3.49 || 4
|-
|}

The words used to describe the patterns in a histogram are: "symmetric", "skewed left" or "right", "unimodal", "bimodal" or "multimodal".

<gallery>
Symmetric-histogram.png|Symmetric, unimodal
Skewed-right.png|[[Skewness#Introduction|Skewed right]]
Skewed-left.png|[[Skewness#Introduction|Skewed left]]
Bimodal-histogram.png|Bimodal
Multimodal.png|Multimodal
Symmetric2.png|Symmetric
</gallery>

It is a good idea to plot the data using several different bin widths to learn more about it. Here is an example on tips given in a restaurant.

<gallery>
Tips-histogram1.png|Tips using a $1 bin width, skewed right, unimodal
Tips-histogram2.png|Tips using a 10c bin width, still skewed right, multimodal with modes at $ and 50c amounts, indicates rounding, also some outliers
</gallery>

The [[United States Census Bureau|U.S. Census Bureau]] found that there were 124 million people who work outside of their homes.<ref>[https://www.census.gov/prod/2004pubs/c2kbr-33.pdf US 2000 census].</ref>  Using their data on the time occupied by travel to work, the table below shows the absolute number of people who responded with travel times "at least 30 but less than 35 minutes" is higher than the numbers for the categories above and below it. This is likely due to people rounding their reported journey time.{{Citation needed|date=August 2010}} The problem of reporting values as somewhat arbitrarily [[rounding|rounded numbers]] is a common phenomenon when collecting data from people.{{Citation needed|date=June 2011}}

[[File:Travel time histogram total n Stata.png|thumb|350px|Histogram of travel time (to work), US 2000 census. Area under the curve equals the total number of cases. This diagram uses Q/width from the table.]]

:{| class="wikitable" style="text-align:center"
|+Data by absolute numbers
|-
! Interval !! Width !! Quantity !! Quantity/width
|-
| 0 || 5 || 4180 || 836
|-
| 5 || 5 || 13687 || 2737
|-
| 10 || 5 || 18618 || 3723
|-
| 15 || 5 || 19634 || 3926
|-
| 20 || 5 || 17981 ||  3596
|-
| 25 || 5 || 7190 || 1438
|-
| 30 || 5 || 16369 || 3273
|-
| 35 || 5 || 3212 || 642
|-
| 40 || 5 || 4122 || 824
|-
| 45 || 15 || 9200 || 613
|-
| 60 || 30 || 6461 || 215
|-
| 90 || 60 || 3435 || 57
|}

This histogram shows the number of cases per [[unit interval]] as the height of each block, so that the area of each block is equal to the number of people in the survey who fall into its category. The area under the [[curve]] represents the total number of cases (124 million). This type of histogram shows absolute numbers, with Q in thousands.
{{clear}}

[[File:Travel time histogram total 1 Stata.png|thumb|350px|Histogram of travel time (to work), US 2000 census. Area under the curve equals 1. This diagram uses Q/total/width (crowding) from the table. The height of a block represents crowding which is defined as  - percentage per horizontal unit.]]

:{| class="wikitable" style="text-align:center"
|+Data by proportion
|-
! Interval !! Width !! Quantity (Q) !! Q/total/width
|-
| 0 || 5 || 4180 || 0.0067
|-
| 5 || 5 || 13687 || 0.0221
|-
| 10 || 5 || 18618 || 0.0300
|-
| 15 || 5 || 19634 || 0.0316
|-
| 20 || 5 || 17981 || 0.0290
|-
| 25 || 5 || 7190 || 0.0116
|-
| 30 || 5 || 16369 || 0.0264
|-
| 35 || 5 || 3212 || 0.0052
|-
| 40 || 5 || 4122 || 0.0066
|-
| 45 || 15 || 9200 || 0.0049
|-
| 60 || 30 || 6461 || 0.0017
|-
| 90 || 60 || 3435 || 0.0005
|}

This histogram differs from the first only in the [[vertical direction|vertical]] scale.  The area of each block is the fraction of the total that each category represents, and the total area of all the bars is equal to 1 (the fraction meaning "all"). The curve displayed is a simple [[density estimation|density estimate]]. This version shows proportions, and is also known as a unit area histogram.
{{clear}}

In other words, a histogram represents a frequency distribution by means of rectangles whose widths represent class intervals and whose areas are proportional to the corresponding frequencies: the height of each is the average frequency density for the interval. The intervals are placed together in order to show that the data represented by the histogram, while exclusive, is also contiguous. (E.g., in a histogram it is possible to have two connecting intervals of 10.5–20.5 and 20.5–33.5, but not two connecting intervals of 10.5–20.5 and 22.5–32.5.  Empty intervals are represented as empty and not skipped.)<ref>Dean, S., & Illowsky, B. (2009, February 19). Descriptive Statistics: Histogram. Retrieved from the Connexions Web site: http://cnx.org/content/m16298/1.11/</ref>