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### Course: 6th grade (Eureka Math/EngageNY) > Unit 6

Lesson 1: Topic A: Understanding distributions- Representing data
- Frequency tables & dot plots
- Creating frequency tables
- Creating dot plots
- Reading dot plots & frequency tables
- Estimate center using dot plots
- Statistical questions
- Statistical questions
- Creating a histogram
- Interpreting a histogram
- Create histograms
- Read histograms

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# Interpreting a histogram

In a cherry pie store, we use a histogram to understand the distribution of cherries on pies. We create buckets for different ranges of cherries, count the pies in each, and can answer questions about our pie inventory and cherry distribution!

## Want to join the conversation?

- Do you agree with me that Sal's pie drawings are great?(58 votes)
- Sal's pie drawings are amazing!(20 votes)

- what is the difference between a histogram and a bar graph(4 votes)
- A histogram shows bars representing numerical values by range of value. A bar chart shows categories, not numbers, with bars indicating the amount of each category.

Histogram example: student's ages, with a bar showing the number of students in each year.

Bar chart example: student's favorite color, with a bar showing the various colors.(37 votes)

- can histograms be used with any set of numbers/data ?(16 votes)
- Histograms can be used with any numbers, it just matters how you label them differently(4 votes)

- So, the height of the bars determine how many we're working with then?(12 votes)
- Yup! Ya thats true
**had to write this much cos' my answer was too brief**(6 votes)

- Who is going to go through a pie and count the exact amount of cherries in that specific pie? For real.(3 votes)
- ⣰⣾⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆

⣿⣿⣿⡿⠋⠄⡀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⣉⣉⣉⡉⠙⠻⣿⣿

⣿⣿⣿⣇⠔⠈⣿⣿⣿⣿⣿⡿⠛⢉⣤⣶⣾⣿⣿⣿⣿⣿⣿⣦⡀⠹

⣿⣿⠃⠄⢠⣾⣿⣿⣿⠟⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄

⣿⣿⣿⣿⣿⣿⣿⠟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠋⢠⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡿⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⠗⠄⠄⠄⠄⣿⣿⣿⣿⣿⣿⣿⡟

⣿⡿⠁⣼⣿⣿⣿⣿⣿⣿⡿⠋⠄⠄⠄⣠⣄⢰⣿⣿⣿⣿⣿⣿⣿⠃

⡿⠁⣼⣿⣿⣿⣿⣿⣿⣿⡇⠄⢀⡴⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠

⠃⢰⣿⣿⣿⣿⣿⣿⡿⣿⣿⠴⠋⠄⠄⢸⣿⣿⣿⣿⣿⣿⣿⡟⢀⣾

⢀⣿⣿⣿⣿⣿⣿⣿⠃⠈⠁⠄⠄⢀⣴⣿⣿⣿⣿⣿⣿⣿⡟⢀⣾⣿

⢸⣿⣿⣿⣿⣿⣿⣿⠄⠄⠄⠄⢶⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠋⣠⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣼⣿⣿⣿⣿⣿

⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣴⣿⣿⣿⣿⣿⣿⣿

⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⣴⣿⣿⣿⣿⠗⠄⠄⣿⣿

⣆⠈⠻⢿⣿⣿⣿⣿⣿⣿⠿⠛⣉⣤⣾⣿⣿⣿⣿⣿⣇⠠⠺⣷⣿⣿

⣿⣿⣦⣄⣈⣉⣉⣉⣡⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⣀⣼⣿⣿⣿

⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⡿⠟(26 votes)

- Can histograms be made sideways? I've seen some bar graphs with horizontal bars instead of vertical ones.(4 votes)
- Yes, and it really depends on the data you want to present and how you want to present it.

Normally, you would use the bar chart (the sideways one), if you want to (and can) sort data in a descending order; for example, if you want to show sales for different brands of food in your store; in this case you will start with the biggest one, and go onwards with the smaller ones.

You would normally use a horizontal chart (the histogram), if your data is naturally sorted - if these are the ranges for probabilities, or if these are sales numbers from a few consequential years, so it doesn't really make sense to sort it ascending or descending. Of course, that's not a strict rule, and much would depend on what do want to show, what purpose do you draw the chart for etc.(9 votes)

- i still don't under stand, this video doesn't help.(5 votes)
- So basically on a histogram, it's a way to graph ranges of data.(3 votes)

- what is the difference between a histogram and a bar graph(3 votes)
- Great question! A histogram is used to represent quantitative data so both the x and y axes have numbers. The x will typically have a range of values while they will have a frequency. On the other hand, a bar graph is used to represent categorical (qualitative) data. So the x-axis will have a label such as color, gender, sports, team, etc. while y will have a frequency.

Graphically you can identify the difference based on the label measures and how the graph is drawn. If there are spaces between bars it is a bar graph and if there are no spaces it is a histogram.

Hope this helps!(6 votes)

- can hisograms be used for hiting people with?(5 votes)
- anything can be if you try hard enough(3 votes)

- when the graph shows that the number of pies and the number of cherries, 0-29, 30-59... does 30-59 means that that eight pies have 30-59, or it has 19, because 59-30=19(3 votes)
- what it means is the numbers that are between and are 30 and 59.

I dont know if I can explain why...

The reason is because first since this is a histogram you would add equations as how many are on this thing. (or maybe it can and I'm just an idiot) Second, I think its mentioned in the video what it means so maybe looking it over would help and I think they would have an explanation for why. Anyways hope this helps?(4 votes)

## Video transcript

Let's say you have a cherry pie store. and you've noticed that there is variability in the number of cherries on each pie that you sell. Some pies might have over 100 cherries, while other pies might have fewer than 50 cherries. So what you're curious about is what is the distribution, how many of different types of pies do you have? how may pies do you have that have a lot of cherries, how many pies that have a few cherries, how many pies are in between? So, to do that, you set up a histogram. what you do is you take each pie in your store, (See I can draw a pie in some kind) it's a cherry pie, I don't know if this is adequate of drawing of a pie. You take each pie in your store, and you count the number of cherries on it. This pie has 1,2,3,4,5 6,7,8,9,10,keep counting Let's say it has 32 cherries. And you are going to do it for every pie. and then you create buckets. Because you don't want to create just a graph I'm not having exactly 32. You just want to get a general sense of things. So you create buckets of 30 you say how many pies have between 0 and 29 cherries? how many pies are between 30 and 59, including 30 and 59? how many pies have at least 60 at most 89 cherries? how many pies have at least 90 at most 119? and then how many pies have at least 120 and at most 149? you know that you don't have any pie that have more than 149 cherries so this should account for everything. Then you count them so for example, 5 pies have more than 30 to 59 cherries and so we create a histogram when you create a histogram, you make this magenta bar go up to 5 so that's how you would construct this histogram that's what the pies at different cherry levels histogram is telling us. so now we have construct it; Let's see if we can interpret it based on the information given in the histogram. So the first question is: based on just this information can you figure out the total number of pies in your store? soon be there all accounted for by this histogram and I encourage you to pause this video and try to figure it out on your own What was the total number of pies? Let's see. There's five pies there's five pies that have ... at least 30 cherries but no more than 59. you have eight pies in this blue bucket you have four pies in this green bucket and then you have ... three pies that have at least 120 but no more than 149 cherries this accounts for all the pies so the total number of pies you have at the store 5 plus 8 plus 4 plus 3 which is what, 5 plus 8 is 13 plus 4,=17, plus 3 is twenty. So there are 20 pies in this store. Then you can ask more a more nuance question. what if you want to know the number of pies with more than 60 cherries the number of pies with more than 60 number of pies with I'll say this 60 or more 60 or more cherries so let's think about it. well this magenta bar doesn't apply because these all have less than 60 but all these other bars are accounting pies that have 60 or more cherries this is 60 to 89, this is 90 to 119 this is a 120 to 149 so it's going to be these eight cherries sorry, these eight pies that are in this bucket plus these four pies, plus these three pies so it is going to be essentially everything but this first bucket everything but all the pies except for these five pies have 60 or more cherries so should be five less than 20 Let's see. 8+4=12,plus 3 is 15 which is five less than 20. So using this histogram we can answer really interest question, which would say how many more pies do we have that have 60-89 cherries than 120 to 149 cherries? We have eight pies at 60-89 60-89 cherries, three that have a 120-149 We have five more pies in the 60 to 89 category that we do in the 120 to 149 categories A lot of questions that we can start to answer hopefully this gives you a sense of how you can interpret histograms.