Data



Reading Data From
Graphs and Charts

When studies are made, the amount of accumulated data can be overwhelming.    This data must be organized so that the study can produce and interpret the desired information.    There are many different ways to organize the data.    The average (or mean), the median, and the mode are three of the ways statisticians organize their data.    The data can be arranged and presented in charts, graphs, or tables.    From these charts, graphs or tables, a quick look can determine the answer to many questions.    The data may come from studies involving science, business, economics, or social science.    The study of this information is a branch of mathematics called statistics.

 

Circle graphs
A circle graph is used when it is desired to show how the whole amount is broken into parts.    The whole circle or pie graph depicts the entire sample space.    The pieces of the pie in the circle graph are called sectors.

 

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Example 1:

The circle or pie graph above, shows the 24 hour schedule of a working mother.

Sector A:    Sleeping:   7 hours.
Sector B:    Getting children ready for school:   1.5 hours.
Sector C:    Driving:   1.5 hours.
Sector D:    Working:   8 hours.
Sector E:    Grocery shopping, cooking, cleaning, laundry:   3 hours.
Sector F:    Reading, bathing, and getting the children for bed:   1.5 hours.
Sector G:    Quiet time:   1.5 hours.

A)   Find the ratio of time spent taking care of the children and the house to the total number of hours in a day.

Solution:
Sectors B, E and F represent the time spent taking care of the children and the house.

The total time spent from sectors B, E and F is:
1.5 + 3 + 1.5 = 6 hours

The ratio of child and the house care to the total number of hours in a day is  

The percentage of the working moms day taking care of the children and the house is 25%.

 

B)   Find the ratio of driving time to working time.

Solution:


The percentage of driving time to working time is 18.8%





Student #1:

Find the ratio of the working mothers quiet time, to the total number of hours in a day.


16/1               1/16               1/24               5/6              


Answer

Example 2:

The following pie graph shows the monthly budget for the Murray family with a yearly income of   $45,000.

A)   How much did the family spend during the given year on medical?

Solution:
Medical is 15% of the families annual income.

What number divided by 45000 equals 15%?

x = (.15)(45,000)

x = $6750

Therefore the Murray family spent $6750 on medical during the given year.

 

B)   How much did the family spend during the year on auto and housing?

Solution:
Auto is 14% and housing is 26% of the annual income.

What number divided by 45000 equals the sum of .14 and .26?

x = (45,000)(.40)

x = $18,000

Therefore the Murray family spent $18,000 during the year on auto and housing.

 







Student #2:

How much money did the Murray family place in savings and spend on food during the year?


$10,200               $5,600               $16,000               $15,300              


Answer




Student #3:

The following is a circle graph which shows the number of students enrolled at a college in different majors.

3a.    What percent of the school's student body are Computer Science majors?


20%               25%               18%               50%              


Answer

3b.    What percent of the school’s student body are English or Art majors?


20%               25%               18%               50%              


Answer

3c.    What is the ratio of History majors to Computer Science majors?


20%               25%               18%               50%


Answer

3d.    What is the percentage of Business majors at this college?


43%               65%               45%               35%              


Answer

Bar And Line Graphs

Bar and line graphs are useful when comparisons are desired.   They are used to measure one set of data against another.    With a Bar and Line graph, one can quickly compare information from one set of data against information from another set.

 

Example 3:

The following data was collected from a business that sells telephone systems.   The bar graph shows the number of phone systems sold, in thousands, during the given years.


Try these questions on your own.   The answers follow.

1.    In what year were the most phone systems sold?

A)   1990         B)   1991         C)   1992         D)   1993         E)   1994

 

2.    In what year were the least number of phone systems sold?

A)   1990         B)   1991         C)   1992         D)   1993         E)   1994

 

3.    When did the largest drop in sales occur?

A)   1990 to 1991             B) 1991 to 1992             C) 1992 to 1993
D) 1993 to 1994

 

4.    When did the smallest increase in sales occur?

A) 1990 to 1991             B) 1991 to 1992             C) 1992 to 1993
D) 1993 to 1994



Answers to problems 1 - 4 are:
B, D, B, D






Student #4:

Double bar graph.
The following graph represents sales for a certain company for the 1st, 2nd, 3rd, and 4th quarters of 1990 and 1991.

Find the following:

4a.    Find the number of sales in the 3rd quarter of 1990.


4,000               5,000               6,000               7,000

5,500


Answer

4b.    Find the number of sales in the 2nd quarter of 1991.


4,000               5,000               6,000               7,000               8,000

Answer

4c.    Find the number of sales in the 2nd and 4th quarter of 1990


10,000               15,000               6,000               11,000               9,000


Answer




Student #5:

The following Line graph depicts sales for two Real estate agents during the years 1990 - 1995.



Find the following:


5a.    Find the number of houses sold by Ms. Smith in 1993.


40               50               30               20               80

Answer

5b.    Find the number of houses sold by Ms. Smith and Mr. Jones in 1992.


50               40               30               20               80


Answer

5c.    In what year did Ms. Smith and Mr. Jones sell the same number of houses?


1990               1991               1992               1993               1994


Answer



Homework


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Student #1:    The answer is B:

Solution:

Find the ratio of the working mothers quiet time, to the total number of hours in a day.


 

The ratio of the mothers quiet time to the total number of hours in a day is 1/16.

If the question would have asked for the percentage, then the following calculations would have been performed:
1/16 = .0625   or   6.25%

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Student #2:    The answer is D:

Solution:
From the annual income, saving is 10% and food is 24%.

What number divided by 45000 equals the sum of .10 and .24?




x = 45000(.34)

x = 15,300

Therefore the amount of money that the Murray family placed in savings and spent on food during the year was $15,300?

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Student #3a:    The answer is A:

 

Solution:

Total number of students:

5250 + 1950 + 1800 + 1500 + 1500 + 3000 = 15,000

Therefore 20%.


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Student #3b:    The answer is B:


Therefore 25%.

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Student #3c:    The answer is D:

Solution:


Therefore 1/2.

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Student #3d:    The answer is D:


Therefore 35%.
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Student #4a:    The answer is D:

7000


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Student #4b:    The answer is B:

5000


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Student #4c:    The answer is D:

11,000


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Student #5a:    The answer is A:

40


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Student #5b:    The answer is B:

40


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Student #5c:    The answer is B:

1991


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