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H. Tables, Charts, and Graphs (Data Interpretation)
 
 


Graphs and charts show the relationship of numbers and quantities in visual form. By looking at a graph, you can see at a glance the relationship between two or more sets of information. If such information were presented in written form, it would be hard to read and understand.

Here are some things to remember when doing problems based on data interpretation:

    1. Take your time and read carefully. Understand what you are being asked to do before you begin figuring.
    2. Check the dates and types of information required. Be sure that you are looking in the proper columns, and on the proper lines, for the information you need.
    3. Check the units required. Be sure that your answer is in thousands, millions, or whatever the question calls for.
    4. In computing averages, be sure that you add the figures you need and no others, and that you divide by the correct number of years or other units.
    5. Be careful in computing problems asking for percentages.
    6. (a) Remember that to convert a decimal into a percent you must multiply it by 100. For example, 0.04 is 4%.
      (b) Be sure that you can distinguish between such quantities as 1% (1 percent) and .01% (one one-hundredth of 1 percent), whether in numerals or in words.
      (c) Remember that if quantity X is greater than quantity Y, and the question asks what percent quantity X is of quantity Y, the answer must be greater than 100 percent

Example Set #28: Table Chart

Examples 1-5 are based on this Table Chart.

The following chart is a record of the performance of a baseball team for the first seven weeks of the season.

 

 

   Games Won
   Games Lost

Total No. of Games Played
 First Week

 5

 3

 8
 Second Week

 4

 4

 16
 Third Week

 5

 2

 23
 Fourth Week

6

 3

 32
 Fifth Week

 4

2

 38
 Sixth Week

 3

 3

 44
 Seventh Week

 2

 4

 50

1. How many games did the team win during the first seven weeks?
(A) 32
(B) 29
(C) 25
(D) 21
(E) 50

Choice B is correct. To find the total number of games won, add the number of games won for all the weeks, 5 + 4 + 5 + 6 + 4 + 3 + 2 = 29.


2. What percent of the games did the team win?
(A) 75%
(B) 60%
(C) 58%
(D) 29%
(E) 80%

Choice C is correct. The team won 29 out of 50 games or 58%.


3. According to the chart, which week was the worst for the team?
(A) second week
(B) fourth week
(C) fifth week
(D) sixth week
(E) seventh week


Choice E is correct. The seventh week was the only week that the team lost more games than it won.

4. Which week was the best week for the team?
(A) first week
(B) third week
(C) fourth week
(D) fifth week
(E) sixth week


Choice B is correct. During the third week, the team won 5 games and lost 2, or it won about 70% of the games that week. Compared with the winning percentages for other weeks, the third week's was the highest.


5. If there are fifty more games to play in the season, how many more games must the team win to end up winning 70% of the games?
(A) 39
(B) 35
(C) 41
(D) 34
(E) 32


Choice C is correct. To win 70% of all the games, the team must win 70 out of 100. Since it won 29 games out of the first 50 games, it must win (70 - 29) or 41 games out of the next 50 games.



Example Set #29: Interpreting Graphs





Answer the following questions based on the graph above.

1. During what two-year period did the company's earnings increase the most?
(A) 95-97
(B) 96-97
(C) 96-98
(D) 97-99
(E) 98-00


Reading from the graph, the company's earnings increased from $5 million in 1996 to $10 million in 1997, and then to $12 million in 1999. The two-year increase from '96 to '98 was $7 million--clearly the largest on the graph. The answer is (C).


2. During the years 1996 through 1999, what were the average earnings per year?
(A) 6 million
(B) 7.5 million
(C) 9 million
(D) 10 million
(E) 27 million

The graph yields the following information:
 Year    Earnings
1996  $5 million
1997   $10 million
1999   $12 million

To figure out the average, add (5 + 10 + 12)/3 = 9. The answer is (C).

3. In which year did earnings increase by the greatest percentage over the previous year?
(A) 96
(B) 97
(C) 98
(D) 99
(E) 2000

 

To find the percentage increase (or decrease), divide the numerical change by the original amount.

 Year

 Earnings

 % increase from year before

 1995

 8

 n/a

 1996

 5

 decrease

 1997

 10

 100%

1999

 12

 20%

1999

 11

 decrease

2000

 8

 decrease
    

The largest number in the right-hand column, 100%, corresponds to the year 1997. The answer is (B).

 

4. If the company's earnings are less than 10 percent of sales during a year, then the Chief Operating Officer will get a 50% pay cut. How many times between 1995 and 2000 did the Chief Operating Officer take a pay cut?
(A) None
(B) One
(C) Two
(D) Three
(E) Four

Calculating 10 percent of the sales for each year yields Year, 10% of Sales (millions), Earnings (millions).

 Year

 10% of sales

 Earnings

is 10% of sales greater than earnings?

 1995

 .10 x 80 = 8

 8

no cut 

 1996

 .10 x 70 = 7

5

 cut

 1997

 .10 x 50 = 5

10

 no cut

 1999

 .10 x 80 = 8

12

 no cut

 1999

 .10 x 90 = 9

11

 no cut

 2000

.10 x 100 = 10

 8

 cut

Comparing the right columns shows that earnings were less than 10 percent of sales in 1996 and 2000. The answer is (C).


 
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