GED Data Analysis Practice

Quantitative problem solving covers about 45 percent of the GED math test, and most of it lives here: percents, ratios, rates, averages, probability, and reading information out of a table or graph.

Question 1 of 23

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A dot plot shows how many books 10 club members read last month: 1 book: 1 dot 2 books: 3 dots 3 books: 2 dots 4 books: 3 dots 6 books: 1 dot What is the mean number of books read?

Data analysis study guide

Data analysis covers the numbers you meet outside a classroom: averages, percents, rates, chances, and charts. These questions reward careful reading more than heavy computation. This guide covers each skill with an example.

Mean, median, mode, and range

The mean is the total divided by the count. The median is the middle value after sorting; with an even number of values, it is the mean of the two middle values. The mode is the most frequent value. The range is the largest minus the smallest.

Know how each reacts to an outlier. One very large value pulls the mean up but barely moves the median, which is why incomes and home prices are usually reported as medians.

Worked example

Find the mean and median of 12, 7, 15, 7, 9, 20.

  1. Sum: 12 + 7 + 15 + 7 + 9 + 20 = 70. Mean = 70 ÷ 6 ≈ 11.67.
  2. Sort: 7, 7, 9, 12, 15, 20. The two middle values are 9 and 12.
  3. Median = (9 + 12) ÷ 2 = 10.5.

Worked example

Four test scores average 82. What score on a fifth test brings the average to 85?

  1. Current total: 4 × 82 = 328.
  2. Needed total for five tests: 5 × 85 = 425.
  3. Fifth score: 425 − 328 = 97.

Percents and percent change

A percent is a number out of 100. To find a percent of a number, convert the percent to a decimal and multiply: 15% of 240 is 0.15 × 240 = 36.

Percent change is (new − original) ÷ original × 100. The denominator is always the original value. A price that goes from $40 to $50 rose 25%, but a price that falls from $50 to $40 dropped 20%. Successive discounts do not add: 20% off and then another 10% off is 28% off in total, not 30%.

Worked example

A jacket costs $80. It is marked 25% off, and then 6% sales tax is added. What is the final price?

  1. Discount: 0.25 × 80 = 20, so the sale price is $60.
  2. Tax: 0.06 × 60 = 3.60.
  3. Final price: 60 + 3.60 = $63.60.

Ratios, rates, and proportions

A ratio compares two quantities, such as 3 cups of flour to 2 cups of sugar. A rate is a ratio with different units, such as 55 miles per hour or $4.20 per pound. A unit rate puts the second quantity at 1, which makes comparison shopping easy.

To solve a proportion, set two equal ratios side by side and cross multiply. Keep the units in the same positions on both sides, or the answer comes out inverted.

Worked example

A recipe uses 3 cups of flour for 24 cookies. How much flour is needed for 40 cookies?

  1. Set up: 3 / 24 = f / 40.
  2. Cross multiply: 24f = 120.
  3. f = 5 cups.

Probability

Probability is the number of favorable outcomes divided by the number of possible outcomes. It is always between 0 and 1. For two independent events, multiply the probabilities. When drawing without replacement, the second probability changes because one item is already gone.

Worked example

A bag holds 4 red and 6 blue marbles. Two are drawn without replacement. What is the probability both are red?

  1. First draw: 4 red out of 10, so 4/10.
  2. Second draw: 3 red left out of 9, so 3/9.
  3. Multiply: 4/10 × 3/9 = 12/90 = 2/15.

Reading tables, bar graphs, and scatter plots

Before reading any values, read the title, the axis labels, and the units. A vertical axis that says “in thousands” turns 45 into 45,000. A scale that starts above zero can make small differences look large.

A scatter plot shows how two variables move together. If points rise from left to right, the correlation is positive; if they fall, it is negative. Correlation alone does not show that one variable causes the other, and the GED likes to test exactly that distinction.

Dot plots, histograms, and box plots

A dot plot puts one dot above a number line for every data value, so a column of four dots above 2 means the value 2 appears four times. The plot is just a list written sideways. To find the total of all values, multiply each value by its number of dots and add. To find the mean, divide that total by the number of dots, not by the number of labels on the axis.

A histogram groups values into intervals of equal width, such as 0 to 9 minutes and 10 to 19 minutes, and the height of each bar is how many values fall in that interval. You cannot read exact values from a histogram, only counts. Questions usually ask how many or what percent fall above or below a cutoff, or which interval holds the median. For a percent, add the bars on the correct side of the cutoff and divide by the total of all bars.

To locate the median on either kind of plot, count from the left. With n values, the median is the value in position (n + 1) ÷ 2, and when n is even it is the average of the two values on either side of that position. The tallest bar or column shows the mode, which is often not where the median sits.

A box plot summarizes data with five numbers: minimum, first quartile, median, third quartile, and maximum. The box spans the middle half of the data, and its width is the interquartile range, Q3 − Q1. A long whisker on one side shows the data is spread out or skewed in that direction.

Worked example

A histogram of 30 delivery times shows these bars: 10 to 19 minutes: 5, 20 to 29 minutes: 11, 30 to 39 minutes: 8, 40 to 49 minutes: 6. What percent of deliveries took 30 minutes or more, and which interval holds the median?

  1. Add the bars at or above 30 minutes: 8 + 6 = 14 deliveries.
  2. Divide by the total: 14 ÷ 30 ≈ 0.467, or about 47%.
  3. The median of 30 values is the average of the 15th and 16th values.
  4. The first bar holds values 1 to 5 and the second holds 6 to 16, so both middle values fall in 20 to 29 minutes.

Counting outcomes and “or” probability

Some questions ask how many outcomes are possible before any probability is involved: how many meal combinations a menu allows, or how many codes a lock can have. Use the counting principle. If one choice can be made in m ways and a second in n ways, the two together can be made in m × n ways. This extends to any number of choices, so a sandwich with 3 breads, 4 fillings, and 2 sauces has 3 × 4 × 2 = 24 versions. A common wrong answer adds the counts, 3 + 4 + 2 = 9, which only counts single choices.

Read whether items can repeat. A code where digits may repeat has 10 choices for every digit. If digits cannot repeat, each spot has one fewer choice than the spot before it, so three different digits give 10 × 9 × 8 = 720 codes.

For the probability of one event or another, count every outcome that fits either condition, but count each outcome only once. When the two conditions overlap, adding their probabilities counts the shared outcomes twice. The fix is to list the outcomes or to subtract the overlap: P(A or B) = P(A) + P(B) − P(both).

A related shortcut is the complement. The probability that something does not happen is 1 minus the probability that it does. For questions with “at least one,” it is often faster to find the chance of none and subtract it from 1.

Worked example

A standard die is rolled once. What is the probability of rolling an even number or a number greater than 4?

  1. Even numbers: 2, 4, and 6, so 3 outcomes.
  2. Numbers greater than 4: 5 and 6, so 2 outcomes.
  3. The 6 is in both lists, so count it once: 2, 4, 5, and 6 are 4 outcomes.
  4. Probability: 4 out of 6, or 2/3. Adding 3/6 + 2/6 = 5/6 would count the 6 twice.

Worked example

A fair coin is tossed 3 times. What is the probability of getting at least one head?

  1. Each toss has 2 outcomes, so there are 2 × 2 × 2 = 8 possible results.
  2. Only one result has no heads: tails, tails, tails.
  3. P(no heads) = 1/8, so P(at least one head) = 1 − 1/8 = 7/8.

Checklist before test day

These skills cover most data analysis items.

  • Find a median for an even-sized list.
  • Work backward from an average to a missing value.
  • Compute percent change using the original value as the base.
  • Set up and solve a proportion with matching units.
  • Multiply probabilities and adjust for no replacement.
  • Read axis units and scale before reading any data point.

Data Analysis practice set 1: 23 questions with answers

Work each question on paper first, then open the answer to check your reasoning.

  1. 1.A dot plot shows how many books 10 club members read last month: 1 book: 1 dot 2 books: 3 dots 3 books: 2 dots 4 books: 3 dots 6 books: 1 dot What is the mean number of books read?

    1. A.3
    2. B.2.5
    3. C.6.2
    4. D.3.1
    Show answer

    Answer: D. 3.1

    Multiply each value by its number of dots and add: 1 + 6 + 6 + 12 + 6 = 31 books. Divide by the 10 members to get 3.1. Choice 6.2 divides by the 5 values on the plot instead of the 10 members.

  1. 2.A histogram shows the wait times of 40 customers: 0 to 4 minutes: 18 5 to 9 minutes: 9 10 to 14 minutes: 7 15 to 19 minutes: 6 In which interval does the median wait time fall?

    1. A.0 to 4 minutes
    2. B.10 to 14 minutes
    3. C.15 to 19 minutes
    4. D.5 to 9 minutes
    Show answer

    Answer: D. 5 to 9 minutes

    The median of 40 values lies between the 20th and 21st. The first bar covers the 1st through 18th values and the second covers the 19th through 27th, so the median is in 5 to 9 minutes. Choice 0 to 4 minutes is the tallest bar, which is the mode interval, not the median.

  1. 3.Lena’s bowling scores in four games were 132, 148, 125, and 155. What must she score in the fifth game for a mean of 145?

    1. A.165
    2. B.145
    3. C.140
    4. D.170
    Show answer

    Answer: A. 165

    A mean of 145 over five games requires 5 × 145 = 725 points. She has 132 + 148 + 125 + 155 = 560, so she needs 725 − 560 = 165. Choice 140 is her current average, not the score she needs.

  1. 4.The mean of six numbers is 20. When one number is removed, the mean of the remaining five numbers is 18. What number was removed?

    1. A.2
    2. B.30
    3. C.20
    4. D.38
    Show answer

    Answer: B. 30

    Six numbers with a mean of 20 total 120, and five numbers with a mean of 18 total 90. The removed number is 120 − 90 = 30. Choice 2 is the change in the mean, not the removed value.

  1. 5.The line of best fit for a scatter plot of study hours (x) and test scores (y) is y = 4x + 58. What score does the model predict for a student who studies 7 hours?

    1. A.65
    2. B.69
    3. C.86
    4. D.90
    Show answer

    Answer: C. 86

    Substitute x = 7: y = 4(7) + 58 = 28 + 58 = 86. Choice 65 adds 7 to 58 without multiplying by the slope.

  1. 6.A scatter plot of 30 cities compares the number of coffee shops with the number of bookstores. The points show a strong positive correlation. Which conclusion is valid?

    1. A.Opening coffee shops causes new bookstores to open nearby.
    2. B.Cities with more coffee shops tend to have more bookstores.
    3. C.Cities with more coffee shops tend to have fewer bookstores.
    4. D.The number of coffee shops is unrelated to bookstores.
    Show answer

    Answer: B. Cities with more coffee shops tend to have more bookstores.

    A positive correlation means the two counts tend to rise together. It does not show that one causes the other, since a third factor such as city population could drive both.

  1. 7.A survey of 160 residents asked about a new bus route. Support: 72 under age 40, 40 age 40 and over Oppose: 18 under age 40, 30 age 40 and over What percent of residents age 40 and over support the route?

    1. A.about 25%
    2. B.about 70%
    3. C.about 36%
    4. D.about 57%
    Show answer

    Answer: D. about 57%

    There are 40 + 30 = 70 residents age 40 and over, and 40 of them support the route: 40 ÷ 70 ≈ 57%. Choice 25% divides by all 160 residents instead of only the 70 in that age group.

  1. 8.A line graph shows a store’s monthly electric bill: January $310, February $285, March $240, April $205, May $230, June $295. Between which two consecutive months did the bill drop the most?

    1. A.February to March
    2. B.January to February
    3. C.March to April
    4. D.May to June
    Show answer

    Answer: A. February to March

    The drops are $25 from January to February, $45 from February to March, and $35 from March to April. Choice March to April ends at the lowest bill, but the drop into March was larger.

  1. 9.A committee of 6 people must choose a chair and a secretary, and one person cannot hold both jobs. How many ways can the two jobs be filled?

    1. A.36
    2. B.15
    3. C.30
    4. D.12
    Show answer

    Answer: C. 30

    Any of the 6 can be chair, leaving 5 for secretary: 6 × 5 = 30. Choice 15 treats the two jobs as identical, but chair and secretary are different roles.

  1. 10.A histogram shows the ages of 60 volunteers: 10 to 19: 9 20 to 29: 15 30 to 39: 12 40 to 49: 10 50 to 59: 8 60 to 69: 6 What percent of the volunteers are 40 or older?

    1. A.24%
    2. B.60%
    3. C.40%
    4. D.30%
    Show answer

    Answer: C. 40%

    Add the bars for 40 and up: 10 + 8 + 6 = 24 volunteers. Then 24 ÷ 60 = 0.40, or 40%. Choice 24% is the number of volunteers, not the percent.

  1. 11.A dot plot shows the number of errors made on 10 data entry shifts: 0 errors: 3 dots 1 error: 4 dots 2 errors: 1 dot 3 errors: 1 dot 9 errors: 1 dot Which statement is true?

    1. A.The median is greater than the mean.
    2. B.The mean is greater than the median.
    3. C.The mean and the median are equal.
    4. D.The mode is greater than the mean.
    Show answer

    Answer: B. The mean is greater than the median.

    The mean is 18 ÷ 10 = 1.8, and the median (the average of the 5th and 6th values) is 1. The single 9 pulls the mean above the median. Choice The mean and the median are equal ignores the effect of that outlier.

  1. 12.A scatter plot compares hours of TV watched per week (x) with hours of exercise per week (y) for 40 adults. The points drift downward from left to right but are widely spread out. Which description fits best?

    1. A.A strong negative correlation
    2. B.A weak positive correlation
    3. C.A weak negative correlation
    4. D.No correlation at all
    Show answer

    Answer: C. A weak negative correlation

    Points that fall from left to right show a negative correlation, and wide spread means it is weak. Choice A strong negative correlation would need the points packed closely around a line.

  1. 13.A clinic recorded flu shots by age group. Under 50: 140 got the shot, 60 did not 50 and over: 210 got the shot, 40 did not What percent of the patients age 50 and over got the shot?

    1. A.60%
    2. B.70%
    3. C.78%
    4. D.84%
    Show answer

    Answer: D. 84%

    There are 210 + 40 = 250 patients age 50 and over, and 210 ÷ 250 = 0.84, or 84%. Choice 60% divides 210 by all 350 patients who got the shot.

  1. 14.A line graph shows a family’s weekly grocery spending: Week 1: $180 Week 2: $205 Week 3: $165 Week 4: $230 Week 5: $195 What is the difference between the greatest and least weekly amounts?

    1. A.$65
    2. B.$50
    3. C.$35
    4. D.$195
    Show answer

    Answer: A. $65

    The greatest amount is $230 in week 4 and the least is $165 in week 3, so the difference is $65. Choice $50 compares week 4 with week 1 instead of with the lowest week.

  1. 15.The mean weight of 8 packages is 12.5 pounds. Two more packages weighing 9 pounds and 17 pounds are added. What is the new mean weight?

    1. A.12.5 pounds
    2. B.12.9 pounds
    3. C.15.75 pounds
    4. D.12.6 pounds
    Show answer

    Answer: D. 12.6 pounds

    The 8 packages total 8 × 12.5 = 100 pounds. Adding 26 pounds gives 126 pounds for 10 packages, so the mean is 12.6 pounds. Choice 15.75 pounds divides by 8 instead of 10.

  1. 16.Which number could be added to the data set 6, 9, 11, 14 without changing its median?

    1. A.10
    2. B.11
    3. C.9
    4. D.12
    Show answer

    Answer: A. 10

    The median now is the mean of 9 and 11, which is 10. Adding 10 gives 6, 9, 10, 11, 14, whose middle value is still 10. Choice 11 would make the new median 11.

  1. 17.A factory makes 420 parts in 6 hours. At the same rate, how many hours will it take to make 1,050 parts?

    1. A.12 hours
    2. B.2.5 hours
    3. C.15 hours
    4. D.17.5 hours
    Show answer

    Answer: C. 15 hours

    The rate is 420 ÷ 6 = 70 parts per hour, so 1,050 ÷ 70 = 15 hours. Choice 2.5 hours is how many times larger the new order is, not the number of hours.

  1. 18.A parking permit code uses 2 letters (A to Z) followed by 2 digits (0 to 9). Letters and digits may repeat. How many different codes are possible?

    1. A.6,760
    2. B.67,600
    3. C.58,500
    4. D.1,296
    Show answer

    Answer: B. 67,600

    Multiply the number of options for each position: 26 × 26 × 10 × 10 = 67,600. Choice 58,500 assumes nothing can repeat (26 × 25 × 10 × 9).

  1. 19.A warehouse shipped a mean of 340 orders per day over 6 days. The first 5 days had 320, 355, 310, 362, and 348 orders. How many orders were shipped on day 6?

    1. A.340
    2. B.345
    3. C.339
    4. D.351
    Show answer

    Answer: B. 345

    Six days at a mean of 340 total 2,040 orders. The first five days total 1,695, so day 6 had 2,040 − 1,695 = 345. Choice 339 is the mean of the first five days.

  1. 20.The mean of four numbers is 15. Three of the numbers are 12, 18, and 9. What is the fourth number?

    1. A.15
    2. B.21
    3. C.13
    4. D.6
    Show answer

    Answer: B. 21

    Four numbers with a mean of 15 total 60, and 12 + 18 + 9 = 39, so the fourth is 60 − 39 = 21. Choice 15 assumes the missing number equals the mean.

  1. 21.A table shows the health plans chosen by employees. Basic: 64 Standard: 112 Premium: 24 What percent of employees chose the Standard plan?

    1. A.44%
    2. B.112%
    3. C.64%
    4. D.56%
    Show answer

    Answer: D. 56%

    The total is 64 + 112 + 24 = 200, and 112 ÷ 200 = 0.56, or 56%. Choice 44% is the percent who chose a plan other than Standard.

  1. 22.A line graph shows monthly museum visitors: March 2,400, April 3,000, May 3,900, June 3,600. What was the percent increase from April to May?

    1. A.30%
    2. B.23%
    3. C.9%
    4. D.90%
    Show answer

    Answer: A. 30%

    The increase is 3,900 − 3,000 = 900, and 900 ÷ 3,000 = 30%. Choice 23% divides by the May count instead of the starting April count.

  1. 23.A paint color mixes blue and white in a ratio of 2 to 5. A painter needs 21 quarts of the mixed color. How many quarts of blue are needed?

    1. A.8.4 quarts
    2. B.15 quarts
    3. C.6 quarts
    4. D.4.2 quarts
    Show answer

    Answer: C. 6 quarts

    The ratio has 2 + 5 = 7 parts, so each part is 21 ÷ 7 = 3 quarts and blue is 2 × 3 = 6 quarts. Choice 8.4 quarts treats blue as 2/5 of the mix instead of 2/7.

More practice sets

Data Analysis has 2 practice sets. None of these questions appear in the full practice tests.

GED percent problems come in three shapes

Nearly every GED percent question is one of three types: find the part (what is 20 percent of 350), find the percent (18 is what percent of 90), or find the whole (12 is 30 percent of what number). Recognizing which of the three you are looking at is most of the work.

Percent increase and decrease deserve separate practice. A $40 item marked down 25 percent is not $25 off. It is $10 off, leaving $30. Compute the change first, then apply it, rather than trying to do both in one step.

Mean and median on the GED math test

The mean is the sum divided by the count. The median is the middle value once the numbers are ordered, or the average of the two middle values when the count is even. The GED frequently asks which measure better describes a data set, and the answer usually turns on whether there is an extreme value pulling the mean away from the center.

Range is the largest value minus the smallest. It is the easiest statistic on the test and one of the most commonly rushed.

Probability and unit rates on the GED

Simple probability is favorable outcomes over total outcomes, reduced to lowest terms. Watch for questions that remove an item without replacing it, which changes the denominator on the second draw.

Unit rate questions ask for a per-one value: miles per hour, cost per ounce, words per minute. Divide the total by the number of units, and check that your answer is stated in the unit the question named.

Frequently asked questions

What kinds of graphs appear on the GED?
Bar graphs, line graphs, circle graphs, scatterplots, and dot plots. You are asked to read values, compare categories, and describe trends.
How much of the test is data analysis?
Quantitative problem solving, which includes data analysis, percents, and ratios, is about 45 percent of Mathematical Reasoning.