Graphs

READING AND INTERPRETING GRAPHS and CHARTS

Graphs and charts play an important part in our society, as they allow us to display and communicate large amounts of data and information in a short time.

Summarizing and interpreting large amounts of information is part of the branch of mathematics called Statistics.

TYPES OF GRAPHS and/or CHARTS:

CIRCLE (PIE) GRAPH:

Used to show parts of a whole. The entire circle represents 100%.

Example of circle graph: Pressure from schoolwork

  1. Describe the pressure from schoolwork that the majority of those surveyed experience?
  1. Overall, according to the above graph, what conjectures can be made about pressure from schoolwork?

BAR GRAPHS:

A bar graph is used to represent two or more things that are similar

From this graph, we are able to compare the number of students in each year quickly.

  1. What is happening to the # of boys and girls as time progresses?
  1. In what year did the total number of students increase the most?
  1. In what year do the girls outnumber the boys for the first time?
  1. Approximately how many total students are there in the year 2002?
  1. What conjectures can we make about the area where this data was gathered in terms of its population?

LINE GRAPHS:

A line graph is used to show changes in one value. In a line graph, only the points are actual data values, but they are connected to show trends in the data.

Example: / Sarah bought a new car in 2001 for $24,000. The dollar value of her car changed each year as shown in the table below.
Value of Sarah's Car
Year / Value
2001 / $24,000
2002 / $22,500
2003 / $19,700
2004 / $17,500
2005 / $14,500
2006 / $10,000
2007 / $ 5,800
The data from the table above has been summarized in the line graph below.

  1. In which year was the value of Sarah’s car the highest?
  1. During which two years did the value of Sarah’s car decrease the most?
  1. How much total depreciation has taken place between 2001 and 2007?

FREQUENCY TABLES:

A frequency table uses tally marks to show the number of pieces of data that fall within given intervals.

Example: The below table shows the weekly $ wages of 25 workers:

  1. The above table is using wage intervals of ______.
  1. How many workers make between $250 and $264?
  1. Which interval reflects the most tally marks?
  1. Is there a way to tell the exact wage amount of each worker using the above table? Explain.
  1. What other observations can you make about the above information? Are there any clusters of data?
  1. What other type of graph would be a good choice to display the above data? Why?

LINE PLOTS:

A line plot is a graph that shows frequency of data along a number line. It is best to use a line plot when comparing fewer then 25 numbers.

Example: The following line plot shows the number of families with one or more children:

  1. How many total families were surveyed?
  1. How many families surveyed have 6 children?
  1. What is the mode of the data?
  1. What is the range of the data?
  1. What is the mean of the data?
  1. Identify any clusters, gaps, or outliersin the above data.
  1. Based on the data, what conjectures can you make about the number of children most families have?

HISTOGRAMS:

A histogram is similar to a bar graph, but there is no space between the bars and each bar represents an interval of data.

Distribution of salaries of the Acme Corporation

In a histogram, the frequency of each response is indicated by the height of the bar. Histograms give us a quick visual representation of the data.

Population Pyramids

  1. Which age group has the highest population for Males? Females?
  1. Approximately, what is the population of males ages 75-79?

STEM and LEAF PLOTS:

Uses place value to represent intervals of data. The # to the left of the vertical line represents the stem while the numbers to the right of the vertical line are the leaves. The leaves always represent the least place value.

Example:

BOX-AND-WHISKER PLOTS:

Used to display a range of data so that one can easily see where the numbers fall. It is useful for identifying clusters of data.

  1. What is the range of the above data?
  1. What is the inter-quartile range?
  1. What is the median?
  1. The “box” represents what percentage of the data?
  1. Is it possible to determine the mean of the above data? Why?

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