Statistics and Probability-Part 7

A data set can be graphed in different ways A data set can be graphed in different ways. A histogram is a general picture of the data. It allows you to see how the data are distributed.

A box plot is a graph in which the data are grouped into four groups of approximately equal size. A box plot gives you a summary of the five values: • the lowest number, or minimum • the middle of the lower half, or first quartile (Q1) • the median • the middle of the upper half, or third quartile (Q3) • the highest number, or maximum

These five values divide the data in four groups, each of which contains about 25% of the data. A box plot shows an overall picture of the data but does not allow you to see details. Box plots are particularly useful for comparing several data sets.

A line graph (graph over time) shows change over a period of time— for example, the change in the length of the bean sprouts from day to day. The graph allows you to look for trends in the data. A description of the data and what you can see in the graph can make interpreting the graph easier. Statements about the center of the data using mean or median and about the spread using range or quartiles can also give insights into the data.

Graphs of data can help you get a better picture of how the data are distributed. Graphs can help you interpret the data and make statements about an experiment.

The graph below represents the height of plants after a seven-day period.

Study the graph. What does the bar at 7 millimeters (mm) represent Study the graph. What does the bar at 7 millimeters (mm) represent? Write three statements about how tall the plants in the study grew.

Ethan says “The mean height of the plants at the end of the experiment is about 10 mm.” Liam says “The mean height of the plants at the end of the experiment is about 15 mm.” Who do you think is right, Ethan or Liam? Which number is most easily found in the graph: the mean, the median, or the mode of the height values? Explain how you might use the information in the graph to find the median height of the plants.

The histograms shown below and on the next page represent the frequency of heights of a group of plants at 10 days, 12 days, and 14 days.

Write down what each histogram tells you about the plant heights Write down what each histogram tells you about the plant heights. Describe the growth pattern of these plants.

Garrett decided to make a line graph of the mean plant height for all of the plants for certain days.

How did he find the height for day 10. What does this point mean How did he find the height for day 10? What does this point mean? When did the plants seem to grow the most? How can you see this on the graph? Comment on the advantages and disadvantages of using Josh’s graph to describe the growth of the plants.

Box plots can be also be used to compare the height of the plants Box plots can be also be used to compare the height of the plants. Remember that a box plot is a graph in which the data are grouped into four groups of roughly equal size. To draw a box plot, you need five numbers from your data: • the lowest number, or minimum • the middle of the lower half, or first quartile (Q1) • the median • the middle of the upper half, or third quartile (Q3) • the highest number, or maximum

Explain what these box plots tell you about the growth of the plants from the 12th to the 14th day. What can you tell about the growth of the plants from the box plots that you cannot tell from the line graph? From the histograms?