Is the number of bins in a histogram the same as the bin width?

Question

I got this question on an assignment (I'm just asking if the number of bins is the same as bin width, not the answer to the homework question) "Many statisticians suggest about 7 bins for a histogram. Try this method out on the datasets for “NBA Team Payrolls” and “Horsepower of Cars”.
What bin width did you choose for each?"

Would that mean 7 bins = bin width being 7?

Answer 1

No.

The number of bins is the number of bars in the histogram

The bin width and number of bins are interrelated, but are not the same.

Data range is the difference between the largest value of the highest bin and the smallest value of the lowest bin.



Bin width equals data range divided by number of bins.

Likewise, data range equals bin width times number of bins and number of bins equals data range divided bin width



Example

Number of bins = 7 and bin width = 50

Bin #1 contains the count of all items between 0 and 50

Bin #2 contains the count of all items between 50 and 100

Bin #3 contains the count of all items between 100 and 150

.

.

.

Bin #6 contains the count of all items between 250 and 300

Bin #7 contains the count of all items between 300 and 350



Data range = 350

Number of bins = 7

Bin width = 50



Bin width = data range ÷ number of bins = 350 ÷ 7 = 50

Data range = bin width * number of bins = 50 * 7 = 350

Number of bins = data range ÷ bin width = 350 ÷ 50 = 7



Additional comment:

1) I would find a histogram with only 7 bars to be of very limited use. The histograms that I use often employ between 100 and 1000 bins. With only 7 bins there is little detail in the histogram.



2) Sometimes the number of bins will be driven by the situation. For example if I were analyzing the colors of a photo, I know that the red, green, and blues values must lie between 0 and 255, so histograms with 256 bins would serve very well. Other times, the bin width may drive the problem. For example, I know that in a certain instrument the digital output value increases in steps of 0.05 volts. It makes no sense to make histogram bins less than 0.05 volts wide, as some bars would necessarily contain only zeros. Histogram bin widths of 0.05 volts, 0.1 volts, 0.25 volts, or other multiple of 0.05 volts would make a useful histogram.



3) The data range does not have to span the entire range of your data. Let's say that most of your data lies in the range from -10 to 10, but some readings in the data are significantly outside that range. Perhaps you have a couple numbers like -55, +72, +20, -15. In most cases you would want to create the histogram so that you can see the detail between -10 and 10 rather than defining a histogram that covers -100 to +100 just so that you can contain your entire range. The points that fall outside the range of your histogram can be counted separately or (more often) included in the bottom bin or the top bin

Answer 2

No. They are not the same. The number of bins is just the number of different categories

that you want to count. The bin width is the range of observations assigned to the bin, and while

you might want to have ranges that are all the same, this is certainly not required.



For example if I were going to make a histogram of the number of cups of coffee people drink in a week, I might have one bin just for people who don't drink coffee at all. Then perhaps a bin with

for 1 through 10, 11 through 20, 21 through 30, and 31 or more.

Answer 3

This question is deceptive. If the question asked about the facets plotted on the ogive graph and now not the features labelled on the dimensions of the x-axis, then the answer is obvious. A factor is plotted alongside the higher class limit. For example, if the cumulative frequency (including the class in query) is 32 and the upper limit of the class is 15, the co-ordinates of the point are x (the variable)=15 and y (cumulative frequency)=32. It is viable that the question has pressured the plotted features with the labels on horizontal axis. Due to the fact that the x-axis is steady, you might be free to decide upon a wise scale and labelling. To make plotting the graph easier, you may make a decision to label the x-axis scale in order that the labels correspond to the features. For example, if the higher limits are 5, 10, 15, 20 and many others. It is wise to label the horizontal axis 5, 10, 15, 20 . . . However there is not any rule about this. Here is a quote from a web based guide on Histograms, that explains that category boundaries are by and large chosen, for simplicity, in order that they coincide with handy scale divisions on the horizontal axis (and the communicate): "via deciding upon corporations beginning at 1 mile and with a width of 1 mile, the boundaries of the companies and the x-axis divisions coincide. This makes introductory examples of the histogram simpler to realise and is in most cases the case in GCSE Maths questions. Commonly, nonetheless, there's no requirement for the boundaries to line up with the scale divisions." Taking all this under consideration, the reply that is by and large anticipated is "a" - the aspects labelled are the higher category limits.

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