4.1 Histograms

Data 4.1 Investigation
Name: _______________
Date: ________
Investigation 4: What Numbers Describe Us? Using Graphs to Group Data
People use numbers to describe a variety of attributes, or characteristics, of people, places, and
things. These attributes include:
· Activities, such as the amount of time it takes a student to get to school
· Performance, such as the number of consecutive times a person can jump rope
· Physical characteristics, such as a person’s height
In this Investigation, you will examine graphs to identify patterns and trends in large sets of data.
Grouping data before graphing makes the data easier to analyze. Your analysis can help you
draw conclusions about the attribute being studied.
4.1: Traveling to School - Histograms
A middle-school class studied the times that students woke up in the morning. They found that
two students woke up almost an hour earlier than the others. The class wondered how much time
it took each student to travel to school in the morning. The table below Shows the data they
collected.
· Based on the data, what three questions do you think the class asked?
·
How might the class have collected that data?
·
What information would a line plot of the data give you? A bar graph?
Data 4.1 Investigation
Name: _______________
Date: ________
You can draw a histogram to display the data in the table. A histogram is a graph that organizes
numerical data into intervals.
Step 1 : Draw a dot plot or make a frequency table to display the data.
The data on student travel vary from 5 minutes to 60 minutes.
· Why is the number line on the dot plot labeled every 5 minutes instead of every minute?
·
How can you identify the data values of the dot plot when the number line is labeled every 5
minutes?
Step 2 : Determine the frequency of the data values that fall into each interval, or group of
consecutive numbers
The height of each bar of the histogram represents the number of data values within a specified
interval, of group of consecutive numbers.
Step 3 : Draw the histogram. The histogram below has and interval size of 10 minutes.
Note : In the histogram below, data values of 10 minutes are graphed in the interval 10~20
minutes, data values of 20 minutes are graphed in the interval 20~30 minutes, and so on.
Data 4.1 Investigation
Name: _______________
Date: ________
·
How is a histogram like a bar Graph? How is it different?
·
How can you use a dot plot or a frequency table to help you make a histogram?
·
What does interval size mean?
·
Using the same data, what would a histogram with a different interval size look like?
Problem 4.1
In the histogram above, the data are grouped into 10- minute intervals. The data could also be
grouped into larger or smaller intervals, Sometimes changing the interval size of the histogram
helps you see different patterns in the data.
A.
1. Make a histogram that displays the travel-time data. Use an interval size of 5 minutes.
2. Compare the histogram above with the histogram you drew in part (1).
How does each histogram help you describe the student travel times?
B.
Which students most likely to wake up the latest in the morning? Explain.
C.
Which students most likely wake up the earliest? Explain.
Data 4.1 Investigation
Name: _______________
Date: ________
D.
1. For the data on travel time, find the mode, the median, the mean, and the range.
Explain how you found these statistics.
2. In what interval does the mode fall? The median? The mean?
E.
Which statistic, the mean or the median, would you choose to report when describing the
average time it takes a student to travel to school? Explain