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A Graph is Worth a 1000 Words
Summary
Data is a collection of facts, such as values or measurements. It can be numbers, words, measurements, observations, or descriptions of things – any kind of information. We usually encounter data that is expressed as a set of numbers. It’s collected in many ways, then organized so that people can make observations about the outcomes.
We usually don’t need to know how the data we’re working with was collected – if that’s important information, it will be provided. However, how data is displayed and interpreted is very important! Once data is collected, it can be displayed in a number of ways. One useful format is a table, another is in a graph, such as a circle, bar, or line graph. You’ve probably seen examples of all of these; they show up in newspapers and in news casts on television.
There are times when it’s very useful to be able to find one value that describes a whole set of data and there are a number of ways to determine that single value. Two common ones are: the mean and the mode. They are values that define the “center” of a set of data or what is typical of the whole set of data. Knowing how to calculate a single value that describes a whole set of data is important!
Workplace Readiness Skill
Mathematics: Uses mathematical reasoning to accomplish tasks.
Workplace Readiness Definition
using mathematical reasoning and processes to accomplish job-specific tasks (e.g., using graphs
and charts to estimate expenditures for a construction job, using decimals and percentages in retail
applications)
making calculations related to personal finance (e.g., wage rates, paycheck deductions, taxes)
Vocabulary
Pie Graph Mean Table Bar Graph Mode Data Line Graph
Context Questions
Have you ever had to do any calculations with decimals?
Can you think of some instances when you used decimals?
Why is important to understand decimals as they relate to money?
Guidelines
1. Prerequisite Knowledge/Skills
You should be able to:
Add, subtract, multiply, and divide using decimals
Add, subtract, multiply, and divide using percents
Add, subtract, multiply, and divide using whole numbers
Define mean, median, and mode
2. Complete the A Graph is Worth a 1000 Words exercise.
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Evaluation
Check your work by referring to the Dollars and Cents - KEY.
Reflection after Completion
Did you solve all or most of the problems correctly?
Which ones were the most difficult for you?
Were you able to apply the technique for solving word problems?
What are the benefits of knowing how to interpret graphs and data?
Resources:
If you need a review or more practice, go to:
http://www.mathsisfun.com/data/data-graph.php
http://www.mathsisfun.com/data/data.html
http://www.mathsisfun.com/mean.html
http://www.mathsisfun.com/mode.html
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A Graph is Worth a 1000 Words
Using information from a graph.
Item # Item
1. Anna did a survey at her school where she asked each child in the school to name their favorite type of pet. Anna decided to present the results in a pie graph.
If there were 800 children in the school, how many said that their favorite pet was fish?
2. Bob surveyed a group of his friends on their favorite type of movie and displayed the data on a bar graph.
You can see which type of movie is the most liked or the least liked at a glance. We see, for example, that the least favorite are romances.
Use the graph to answer these two questions:
A. How many people say that their favorite type of movie is SciFy?
B. What is the mode of the distribution?
(Remember that the mode is value or category that appears most often in a set of data.)
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3. The population of a town was recorded every twenty years from 1900 to 2000. The results are shown in the line graph below. Use the graph to answer these three questions:
A. What was the population of the town in the year 1900?
B. How much did the population increase between 1960 and 1980?
C. Assuming the trend in the population growth continues, what will be the population in 2020?
4. This table shows some data that scientists have collected about our solar system.
Planet Mass
(in relation to Earth) Distance from the Sun (in AU)
Mercury 0.4 0.06
Venus 0.7 0.8
Earth 1 1
Mars 0.1 1.5
Jupiter 318 5.2
Saturn 95 9.5
Neptune 14 19.2
Uranus 17 30.0
Which conclusion does the data support?
A. Three planets in the solar system have less mass than Earth.
B. Earth is the only planet on which people can live.
C. Some planets in the solar system are more than 500 AUs from the sun.
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5. The Maple Avenue Diner does a great business at lunch time. The owner graphed the breakdown of
the percentage of sales of each type of item on the menu. Using the pie chart, answer the following
questions:
A. If 15% of the sales were desserts, how much of the lunch
sales were for desserts?
B. Which of the following percentage is the best estimate of
sandwich sales?
a. 15%
b. 21%
c. 40%
d. 65%
6. Your boss asked you to create a bar chart of the total sales of loaves of bread in the bakery by month
for the last January through June. After she looked at your chart, she asked, “What is the mean
number of loaves that we’ve sold during this period of time?”
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A Graph is Worth a 1000 Words - KEY
Using information from a graph.
Item # Item
1. Anna did a survey at her school where she asked each child in the school to name their favorite type of pet. Anna decided to present the results in a pie graph.
If there were 800 children in the school, how many said that their favorite pet was fish?
SOLUTION: First determine what percent of the
children said that their favorite type of pet is fish by
adding all the given percentages then subtracting that
number from 100%
6% + 7% + 28% + 36% + 8% + 11% = 96%
100% − 96% = 4%
Now calculate 4% of 800 (the number of children at
the school.
4% of 800 = .04 × 800 = 32.00
32 children said their favorite pet was fish.
2. Bob surveyed a group of his friends on their favorite type of movie and displayed the data on a bar graph.
You can see which type of movie is the most liked or the least liked at a glance. We see, for example, that the least favorite are romances.
Use the graph to answer these two questions:
A. How many people say that their favorite type of movie is SciFy?
SOLUTION: 4 people.
B. What is the mode of the distribution?
(Remember that the mode is the value or category that appears most often in a set of data.)
SOLUTION: 6 (Drama) is the mode since it occurs the most.
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3. The population of a town was recorded every twenty years from 1900 to 2000. The results are shown in the line graph below. Use the graph to answer these three questions:
A. What was the population of the town in the year 1900?
B. How much did the population increase between 1960 and 1980?
C. Assuming the trend in the population growth continues, what will be the population in 2020?
SOLUTION:
A. What was the population of the town in the year 1900?
1000
B. How much did the population increase between 1960 and 1980?
The population in 1960 was 3000.
The population in 1980 was 3500.
Subtract to find the increase:
3500 – 3000 = 500
C. Assuming the trend in the population growth continues, what will be the population in 2020?
The population increased by 500 from 1960 to 1980 and by 500 from 1980 to 2000.
The trend is an increase of 500 in 20 years.
If the trend continues, the population in 2020 will be 4500.
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4. This table shows some data that scientists have collected about our solar system.
Planet Mass
(in relation to Earth) Distance from the Sun (in AU)
Mercury 0.4 0.06
Venus 0.7 0.8
Earth 1 1
Mars 0.1 1.5
Jupiter 318 5.2
Saturn 95 9.5
Neptune 14 19.2
Uranus 17 30.0
Which conclusion does the data support?
A. Three planets in the solar system have less mass than Earth.
B. Earth is the only planet on which people can live.
C. Some planets in the solar system are more than 500 AUs from the sun.
SOLUTION: When determining which conclusion the data supports, remember to look only at the
information in the table – don’t make assumptions that aren’t supported by the data.
A. Looking at the numbers, there are 3 planets (Mercury, Venus, and Mars) with a mass that
is less than Earth’s. The data support conclusion “A”.
B. This may be a true statement, but none of the information in the table supports this as a
conclusion.
C. Look at the numbers in the column labeled “Distance from the Sun” … all of the numbers
are less than 500. The table doesn’t support this conclusion.
Only conclusion “A” is supported by the data.
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5. The Maple Avenue Diner does a great business at lunch time.
The owner graphed the breakdown of the percentage of sales
of each type of item on the menu. Using the pie chart, answer
the following questions:
A. If 15% of the sales were desserts,
how much of the lunch sales were
for desserts?
SOLUTION: Looking at the graph, you see that
there was a total of $2,000 in lunch sales,
calculate 15% of $2,000:
15% of $2,000 = .15 × 2,000 = 300.00 or $300
B. Which of the following percentage is
the best estimate of sandwich sales?
a. 15%
b. 21%
c. 40%
d. 65%
The easiest way to estimate the percentage of
sandwich sales is to look at the options and
select the most reasonable answer.
Looking at the pie graph, you can see that the
segment for “Sandwiches” is the largest
segment and is close to half (50%) of the chart
… so the answer can’t be “a” or “c” since they
are much smaller than 50%. Option “d” (65%)
is larger than half, so that can’t be the answer
either.
The correct answer is “c” or 40%.
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6. Your boss asked you to create a bar
chart of the total sales of loaves of
bread in the bakery by month for
the last 6 months. After she looked
at your chart, she asked, “What is
the mean number of loaves that
we’ve sold during this period of
time?”
SOLUTION: To calculate the mean of this set of data, total the number of loaves sold, then divide
by the number of months. Look at the graph to get the number of loaves sold each month:
January: 80 March: 60 May: 50
February: 85 April: 90 June: 70
Add the number of loaves sold and divide by 6:
(80 + 85 + 60 + 90 + 50 + 70) ÷ 6 = 435 ÷ 6 = 72.5
The mean (average) number of loaves sold each month is 72.5.
