PowerPoint Presentation

HistogramsKevin Zhou, Joshua Zhong, and Daniel FalvoWhat is a histogram?Is it like 1000 times less than a milligram?

1 mg

No. It is a diagram that displays the frequency of a continuous independent variable, or a series of intervals. It displays how many data points lay in each interval.Does this sound boring?

Well... if so... you have 5 seconds to fall asleep.54321

How do you interpret histograms?

TitleIntervals, X-AxisFrequency, Y-AxisNumber of events in a given interval

But when?But when should you use histograms instead of these?

When to appropriately use histogramsWhen you have only one independent variable, you should use histograms.If you have very large data sets, use histograms to summarize them graphically.

What do histograms look like? (For real)

Are you my kind?Unless there are outliers.???Symmetrical histograms are shaped like mounds.Example of outliers

Am I an outlier?

I think.How can histograms be used in real life?Example: How many people arrive at a certain time at the car loop on a two hour delay schedule?

Independent variable: When people arriveDependent variable: How many people arrived

Notice how the data is NOT categorical, even though each interval seems like one! They have numbers, and thus, they are numerical.What type of data is necessary to make a histogram?NUMERICAL!!!THE HISTOGRAMAmount of studentsWhen kids arrive when there's a two hour delayHow is this histogram meaningful?This histogram is meaningful because it shows that most people arrive at the car loop early in the case of a two hour delay, so the teachers should pay the most attention from 10:00 to 10:03.

What have we seen so far?All of the histograms that weve seen so far are called frequency histograms.

To create a histogram, first make a data table; then, just make the histogram as you would make a bar graph. Remember, the difference between them is very slight. Histograms have the rectangles next to each other; the other has them separated. Histograms have numerical independent variables. Bar graphs have categorical independent variables.

How do you create a histogram?Decide on an example.Collect data and put it in a data table.As if making a bar graph, make a rectangle above each interval to the dependent variable.There is no step 4.Label the X-axis and Y-axis.Give your graph a title.Format it however you want, and in the meantime, set the gaps of the bars to 0%.Stare at your masterpiece.DONE!

Relative frequency histogramHow can we make a relative frequency histogram using the information from the frequency histogram?

Both histograms look the same because the relative frequency histogram shows the proportion of data in each interval.

How do you create a relative frequency histogram?Decide on an example.Collect data.Add up each independent variable.Divide each data point by the number you got from step 3. Record all of those numbers into a data table.As if making a bar graph, make a rectangle above each interval to the dependent variable.Label the axes and give your graph a title.Do all of your pretty formatting techniques.Stare at your masterpiece.DONE! AGAIN!

NOTICED HOW BOTH ARE 9 SIMPLE STEPS?

Rounded to the nearest hundredth due to space issuesInterpreting relative frequency histograms (AKA Probability histogram) Probability, Y-Axis0.4 means that there is a 40% chance, that someone would arrive between 10:00-10:01.How does this relate to statistics?What is probability?Probability is the relative frequency of an event in the long run.This means that in the long run, the relative frequency histogram should look the same as a probability histogram!(Probability histograms are where all of the bar heights add up to 1)Summing up relative frequency!Relative frequency is an events probability, or the proportion of times the event occurs in the long run.Advantages and DisadvantagesAdvantagesThey are very easy to read, and are thus great for comparing data.They can show the shape of distribution for a larger set of data.They show trends in the data clearly.DisadvantagesThe original data cannot be derived from the graph. That is because the graph only shows the frequencies. The intervals can combine several data points together, so you cant retrieve the original data.It is hard to read when there are outliers.Remember the outliers!

OrderWhen used in histograms, order just means how the graph is arranged in sequence.For example: The X-axis is arranged in arrival time.Interval sizeThe interval size is a mini-range. Anything that is between the minimum and maximum of two adjacent intervals will all be summed up into one bar.To select an interval size, it is suggested to find the range of the whole data set (maximum minimum) and divide this number by 10.Decreasing interval sizeWhen you decrease interval size, the histogram will look different. The bars will have lower frequency.

Interval size 1Interval size 5Problem based off the graphWhere is the outlier on this histogram?Also known as: A pop quiz!The answer is After. Notice the jump between 10:10 and After.The reason why 10:00-10:01 is not the correct answer is because if we extended the histogram like so...If you imagine that there was more data to the left, wouldnt it be like a regular bell-curve?Some people would arrive right on the spot, while others would arrive 15 minutes early.Works Cited or ConsultedThe Cartoon Guide to Statisticshttp://www.shodor.org/interactivate/activities/Histogram/Howto_histogram.pdfhttp://www.studyzone.org/mtestprep/math8/k/histograms5l.cfmhttp://www.psychstat.missouristate.edu/introbook/sbk09m.htmDavid, H. A.; Nagaraja, H. N. (2003).Order Statistics. Wiley Series in Probability and Statistics.