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Histograms & Box Plots
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What you will learn from this videoWhat you will learn
- 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 Video
What 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 20-year ranges. Different ranges can lead to different conclusions about the data.
After Video
In a graph, what are outliers?ANSWEROutliers 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 40-60 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
Equally-spaced 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.
- y-axis DEFINE
The vertical axis. In histograms, it shows the number of values in a range.
- x-axis 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
- Practice Word Problems
- Practice Number Problems
- Lesson Plan
- Teacher Guide