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Histograms & Box Plots
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 We’ll learn about histograms.
 We'll also learn about box plots.
 And we'll see how this knowledge can help us visit an amusement park, bike long distances and take care of animals!

Discussion Questions
 Before VideoWhat is the first step you must take before interpreting or graphing this data set?
3, 13, 4, 6, 6, 7, 12, 10ANSWERI should first sort the data in ascending order (from least to greatest).
3, 4, 6, 6, 7, 10, 12, 13ANSWERThe median is the number in the middle. I can find it by crossing out one number at a time from both the left and right sides until I find the middle. Because there is an even number of values, I have to find the average of the two numbers in the middle. (6 + 7)/2 = 6.5. The median is 6.5.
A line plot with one point over 1, four points over 4, one point over 6, two points over 7, one point over each of 14, 16, 31, 36, 47, 48, 50, and 68, two points over 71, and one point over 74.
ANSWERIt does not make sense to say that most people are 4 years old, because only 4 out of 19 people are 4 years old. I can say that the age with the greatest frequency is 4.
I could split up age groups by kids, parents, and grandparents. Or I could split them up into 10 or 20year ranges. Different ranges can lead to different conclusions about the data.
 After VideoIn a graph, what are outliers?ANSWER
Outliers are data points that are not common and far away from the range with the greatest frequency.
The largest number of people are in the 4060 range. The least number of people are between 20 and 40. Maybe the people who got married are in their 40s, and they or their friends have some children.
I could increase the number of bins, and then I might know more about the ages of people in attendance.
Box plots tell me the least and greatest value in the data, as well as the median. They also tell the lower and upper quartile. Those values can only be estimated from histograms.
First, I find the median by counting data values from the left and right sides toward the middle until I reach one or two numbers in the middle. To find the lower quartile, I do the same thing between the least value and the median, and to find the upper quartile, I find the middle between the median and the greatest value. It makes sense because the median cuts the data in half, and if I cut it in half one more time, I get quarters!

Vocabulary
 Line plot DEFINE
A plot that gathers data on a number line.
 Bins DEFINE
Equallyspaced intervals that we use to sort data on a graph.
 Bar graph DEFINE
A graph that represents data using vertical or horizontal bars.
 Histogram DEFINE
A type of bar graph that displays ranges of data.
 yaxis DEFINE
The vertical axis. In histograms, it shows the number of values in a range.
 xaxis DEFINE
The horizontal axis. In histograms, it shows the range of measurements for each bin.
 Outliers DEFINE
Data sets or points that are not common and far away from the rest of the data set.
 Median DEFINE
The number in the middle of a sorted data set.
 Lower quartile DEFINE
A value, to the left of which 25% of the data lies.
 Upper quartile DEFINE
A value, to the right of which 25% of the data lies.
 Interquartile range DEFINE
50% of the data, which lies between the lower and upper quartiles.
 Line plot DEFINE

Reading Material
Download as PDF Download PDF View as Seperate PageWHAT ARE HISTOGRAMS AND BOX PLOTS?Histograms are a special kind of bar graph that shows a bar for a range of data values instead of a single value. A box plot is a data display that draws a box over a number line to show the interquartile range of the data. The ‘whiskers’ of a box plot show the least and greatest values in the data set.
To better understand histograms & box plots…
WHAT ARE HISTOGRAMS AND BOX PLOTS?. Histograms are a special kind of bar graph that shows a bar for a range of data values instead of a single value. A box plot is a data display that draws a box over a number line to show the interquartile range of the data. The ‘whiskers’ of a box plot show the least and greatest values in the data set. To better understand histograms & box plots…LET’S BREAK IT DOWN!
What are histograms?
If a data set has a lot of different measurements, displaying it using line graphs does not always help to interpret the information. Instead, you can display the data using a type of bar graph called a histogram. In a histogram, bars represent ranges instead of individual values. These bars are called bins, and they are presented continuously with no spaces between them. Each bar represents a range of data points, and the height of the bar tells us how many data points are in that range. Now you try: Find a picture of a histogram online or in your textbook. Identify the bins and the height of each bar.
What are histograms? If a data set has a lot of different measurements, displaying it using line graphs does not always help to interpret the information. Instead, you can display the data using a type of bar graph called a histogram. In a histogram, bars represent ranges instead of individual values. These bars are called bins, and they are presented continuously with no spaces between them. Each bar represents a range of data points, and the height of the bar tells us how many data points are in that range. Now you try: Find a picture of a histogram online or in your textbook. Identify the bins and the height of each bar.What can we learn from reading a histogram?
On a test, the students on your class got the following scores: 58, 55, 58, 55, 59, 56, 54, 62, 66, 62, 62, 61, 68, 70, 66, 70, 69, 66, 63, 70, 66, 66, 62, 61, 76, 77, 71, 75, 71, 79, 79, 78, 85, 88, 85, 81, 85, 86, 95, 99, 91, 95. You can separate the data into ranges. Here, it makes sense to choose ranges 5059, 6069, 7079, 8089, and 9099. You want to have enough bins to make several distinct ranges, but not so many that they are hard to interpret. If you look at the histogram represented by the data, you can see that the most common grades are in the 6069% range. The least common grades are in the 90100% range. Those are called outliers. Now you try: Find a picture of a histogram online or in your textbook. Which bin contained the least number of values? Where there any outliers?
What can we learn from reading a histogram? On a test, the students on your class got the following scores: 58, 55, 58, 55, 59, 56, 54, 62, 66, 62, 62, 61, 68, 70, 66, 70, 69, 66, 63, 70, 66, 66, 62, 61, 76, 77, 71, 75, 71, 79, 79, 78, 85, 88, 85, 81, 85, 86, 95, 99, 91, 95. You can separate the data into ranges. Here, it makes sense to choose ranges 5059, 6069, 7079, 8089, and 9099. You want to have enough bins to make several distinct ranges, but not so many that they are hard to interpret. If you look at the histogram represented by the data, you can see that the most common grades are in the 6069% range. The least common grades are in the 90100% range. Those are called outliers. Now you try: Find a picture of a histogram online or in your textbook. Which bin contained the least number of values? Where there any outliers?How can we organize our data for a histogram?
When you have a lot of data, you first have to decide how many bins you would like to use, and what the range of each bin should be. In a bike race, the distances in kilometers that cyclists rode are: 5, 8.25, 15.5, 18, 20, 22.5, 28, 28, 29.5, 30, 30, 36.5, 38, 42.5, 45.75, 46, 47, 48, 48, 50, 50, 52, 55, 58, 58, 59, 63.25, 65.5, 67, 70, 70, 72, 75, 75, 76, 83, 87.75, 94.5, 95. You can organize the data into 5 bins, the first one 019, then 2039, 4059, 6079, and 8099. You can then draw the axes for the graph and label the bin sizes at the bottom along the xaxis, and label it “Distance Biked.” The yaxis can be labeled “Number of Cyclists.” Now as you read the data, you can make a tick to count each time a point contributes to a bin. The 019 bin has a frequency of 4, 2039 has 9, 4059 has 13, 6079 has 9, and 8099 has 4. You can see that the most common distance biked is 4059 kilometers! If you choose bin size 5, you would have a lot more bars and they would be harder to interpret. If you choose bin size 40, you would only have 3 bars, which is not clear either. It is important to choose a bin size that helps you make sense of the data. Now you try: A data set contains the following data: 12, 18, 19, 5, 17, 10, 3, 2, 24, 1, 22. What size bins would you choose for your histogram?
How can we organize our data for a histogram? When you have a lot of data, you first have to decide how many bins you would like to use, and what the range of each bin should be. In a bike race, the distances in kilometers that cyclists rode are: 5, 8.25, 15.5, 18, 20, 22.5, 28, 28, 29.5, 30, 30, 36.5, 38, 42.5, 45.75, 46, 47, 48, 48, 50, 50, 52, 55, 58, 58, 59, 63.25, 65.5, 67, 70, 70, 72, 75, 75, 76, 83, 87.75, 94.5, 95. You can organize the data into 5 bins, the first one 019, then 2039, 4059, 6079, and 8099. You can then draw the axes for the graph and label the bin sizes at the bottom along the xaxis, and label it “Distance Biked.” The yaxis can be labeled “Number of Cyclists.” Now as you read the data, you can make a tick to count each time a point contributes to a bin. The 019 bin has a frequency of 4, 2039 has 9, 4059 has 13, 6079 has 9, and 8099 has 4. You can see that the most common distance biked is 4059 kilometers! If you choose bin size 5, you would have a lot more bars and they would be harder to interpret. If you choose bin size 40, you would only have 3 bars, which is not clear either. It is important to choose a bin size that helps you make sense of the data. Now you try: A data set contains the following data: 12, 18, 19, 5, 17, 10, 3, 2, 24, 1, 22. What size bins would you choose for your histogram?