How to Draw a Histogram by Hand

Using a small data set, in this video I show you how to make a frequency distribution and the corresponding histogram by hand. While technology is preferable, it is useful to do this by hand once to see how the graph works. You can read more about these graphs here: www.mathbootcamps.com/making-f....
Note: This video is from a course I am teaching through my college but I share it in case others find it helpful! Any section numbers mentioned match up with the textbook "Business Statistics 8th edition - Groebner".

[@ppavic7]

Thank you so much for this lesson. Great.

[@asdfghjkl45245]

THIS IS NOT A HISTOGRAM, this is a bloody bar graph!

[@mamadetaslimtorabally7363]

Excellent video tutorial. (from Mauritius)

[@BucketManDBD]

Very easy to understand. Thank you.

[@emilyjones5528]

Thank you, this really helped me a lot

[@connorludwig1447]

histogram shows up at 5:35 if you want to skip frequency distribution

[@thechipbag9762]

Thank you very much! Very helpful!

[@asifjaved7537]

Thanks a lot . Very smooth explained each step. 🌝🤗

[@freeflightguy2109]

what if the classes are of different widths eg 2-4 then 4-9?

[@shinh4221]

Thanks have to do one like this with raw data for my lab, wasn't sure how the classes were determined

[@New_332]

Nicely explained

[@aprilalfaro4964]

Where are the boundaries ?

[@teamirving.11]

Thank you, but you could've included the appropriate measures of central tendency and variability as well. That would've been even more helpful

[@littleblackdress8239]

I’m confused why you divide by 6 in the beginning ? Is it always going to be 6?

[@narektheking9205]

Thank you so much

[@jaml4950]

thank you so much

[@tedjuniorostervall1827]

Thank you for making this video tutorial, however I do want to point out that this is not a histogram, but a simple bar graph. When making a histogram you would need to do as you have, but additionally find the center of each class by subtracting 32 - 24, 40 - 32 and so on. After that you would need to divide the frequency with the different class-borders to find the hight of the columns. I have chosen to use another data-material for my exercise, but you would do as followed. 160 - 150 = 10 The first centerpoint is 10. Divide the frequency with the center. My frequency is 28 and therefor I take 28 : 10 which is 2.8. 2.8 equals the hight of the column. After that you would draw the different class-borders into a normal axis and you would then use the hight which would be 2.8 for the first and then depending on whatever calculations you have made.

[@MathBootcamps]

Hmmm. This is certainly a histogram in the "classical statistics" sense (check any elementary level textbook) although I do concede that there are other types. I am not familiar personally familiar with the type of histogram you describe but that doesn't mean it doesn't exist!! It IS important to make a distinction between this and a bar graph however as they are not the same! A bar graph is generally used for understanding the frequencies associated with categorical variables (such as eye color, or vehicle type). In a bar graph, the order of the bars doesn't have meaning nor does the distance between each bar. This means that we can't really use a bar graph to talk about "shape, center, and spread" like we do with a histogram. A histogram LOOKS like a bar graph but is actually much different. First, the underlying variable is quantitative (such as height or weight). Secondly, the distance across bars has meaning (in this case the class width) and the bars touch to indicate that all values are covered. The bars have a particular order and therefore the concept of "shape" can be used to understand the data. For example, if a histogram is bell shaped/symmetric then we can apply things like the empirical rule etc. I know my explanation probably went longer than it should but I'm hoping it will help others when they are comparing a histogram and a bar chart. Again, they look similar but are actually very different!

[@tedjuniorostervall1827]

sinuss2.cappelendamm.no/c383087/artikkel/vis.html?tid=959908

[@MathBootcamps]

Awesome, I will check that out!

[@chiknosis]

Appreciate it

[@gregl2249]

awesome

[@Dylan-se2hs]

She forgot to add 1 when going to the next class

[@aliyankhan4749]

why divided by 6

[@grantgilbert6575]

yes like how the heck do you know the number of classes

[@hanxxiyeoreumikim1987]

hi! i'm in 7th grade and this is our lesson for this quarter.. but it seems that you and my teacher have different 'methods' especially in the table of classes and frequency.. she told us that the desired number of class intervals, or the "8" you used in the video should be subtracted to 1 and add it to the lowest class intervals or the numbers in the left side.. And one more thing, she also told us not to overlapped the class intervals.. What you did in the video is: 24 - 32 32 - 40 But based on our discussion, it should be: 24 - 32 33 - 41 i'm confused about this and i hope you can explain this.. Anyway, i know that this is all about histogram (i'm not sure, but I think it's just a simple bar graph).. i just want to clear things up ... thank you.. :)

[@MathBootcamps]

Hi! It is true, there are different methods for approaching this. Im not too familiar with the different way you were describing to get the classes (but it sounds fine). However, I can comment a bit on overlapping vs. not overlapping. Sometimes, when the data does not include decimal values, you will see that a frequency distribution is not made with the end values overlapping (as you did). With data that includes decimal values, we need the groups overlapping to allow for values such as 31.9994 etc. that would have "no place to go" otherwise. If there aren't decimal values, you could still do it with the overlapping groups (although remember that they are not truly overlapping as the right hand endpoint is not included) or you could set up the groups the way you have, starting at a new number each time. In stats, especially with graphs/plots, there is a surprising amount of "wiggle-room" with how things are done. There is a standard overall idea (here it is "group the data and find the frequency") and then slightly different ways to implement it! This video follows the most common method seen in college textbooks right now. So your method is still quite valid! Hope this helps! Jerimi

[@hanxxiyeoreumikim1987]

oh, thank you for your quick reply.. :) yeah, maybe I need to wait for more years to study about the different methods.. like what you said, that method is found in college books.. but I'm still in my freshman year in high school so.. it can be really hard for me to understand.. By the way, thank you for the information you gave me.. i'm pretty sure I can use these things in the future.. Thank you again, and keep up the good work in making video like this.. :D

[@nicholelemus9304]

what do you do if there is a zero in the frequency table???? need answer immediately!!!

[@cuprisun]

I don’t get it....

[@Iceytiger181]

You are doing it wrong. It's incorrect because when you started to make your frequency distribution your suppose to add 8 but start counting with the number say it's 40 and add another 8 that would be 47 because ur counting with the first number.

[@MathBootcamps]

Iceytiger181 I think you might be thinking of a different method? We are actually adding the class width to the first number each time, so there is no need for overthinking. We just need to add 40 and 8 (using your example) to get 48. Remember that the right hand endpoint is not included in the range of possible values for that class (as that can cause confusion as well). There are other methods for making these plots though that use a different style of class width. This just happens to be the most common.

[@Iceytiger181]

kk....

[@adrienneblalock5848]

hah bitch gottem

[@aprilalfaro4964]

Gee a bit sloppy if you asked me thanks tho

[@adrienneblalock5848]

leave her alone she's trying her best