Algebra, Geometry and Other Math: Data, Graphs and Probability
Tables, bar and line and circle graphs, frequency tables built from tallies, mean and median, trends and inferences, and probability as a branching tree.
8 topics · 38 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Reading Tables
- How it worksHow do you pull one value out of a table by crossing a row with a column?
- Worked exampleFind Tuesday's total when a table lists 14 apples, 9 pears and 22 plums sold that day.
- Worked exampleFind the largest temperature swing among highs of 72, 65 and 80 with lows of 51, 49 and 62.
Your turneasy1 of 3
A table of Tuesday's sales lists 25 apples, 17 pears and 42 plums. How many pieces of fruit were sold that day?Bar Graphs and Picture Graphs
- How it worksHow does the height of a bar turn into a value using the scale printed up the side?
- Worked exampleFind the value of a bar that stops exactly halfway between the 40 and 60 gridlines.
- Worked exampleFind the total when a picture graph shows three and a half symbols worth 20 things each.
- Common mistakeWhy does a bar graph whose scale starts at 90 instead of 0 exaggerate the differences?
- Going furtherWhat happens to a picture graph when its key changes from 10 per symbol to 100 per symbol?
Your turnmedium1 of 3
A bar stops exactly halfway between the gridlines marked 48 and 109. What value does it show?Line Graphs and Circle Graphs
- How it worksHow does the steepness of a line graph segment show how fast something is changing?
- How it worksHow does a circle graph turn percents into wedges, with 25 percent becoming a quarter turn?
- Worked exampleFind the number of degrees in a pie slice standing for 30 percent of a budget.
- Worked exampleFind how many of 250 students chose pizza when its pie slice covers 40 percent.
- Going furtherWhat can a circle graph never tell you that a bar graph of the same data can?
Your turnmedium1 of 3
A circle graph shows a slice standing for 62 percent of a budget. How many degrees does that slice cover? Round to two decimal places.Frequency Tables and Tally Marks
- How it worksHow does a frequency table turn a messy list of results into a count for each value?
- How it worksHow do the bars of a histogram grow straight out of the counts in a frequency table?
- Common mistakeWhy isn't the tallest bar in a frequency chart the same thing as the average value?
- Worked exampleFind the most common shoe size when sizes 6, 7, 8 and 9 have counts of 3, 8, 5 and 2.
- Worked exampleFind how many students were surveyed when the four frequencies come to 3, 8, 5 and 2.
Your turneasy1 of 3
A frequency table lists four values with frequencies of 3, 8, 5 and 16. How many people were surveyed altogether?Mean, Median, Mode and Range
- How it worksHow does the median find the middle by sorting first, and what do you do with an even count?
- How it worksHow does the mean balance a set of values like weights sitting on a seesaw?
- Worked exampleFind the mean, median, mode and range of 4, 7, 7, 9 and 13.
- Common mistakeWhy isn't the median simply the number halfway between the smallest and the largest?
- Worked exampleFind the median of 3, 8, 12, 15, 20 and 21.
Your turneasy1 of 3
Find the mean of 4, 7, 7, 9 and 27. Round to two decimal places.Trends and Inferences
- How it worksHow do you read a trend by following the overall direction instead of every little bump?
- How it worksHow far past the last data point can you safely predict before it turns into a guess?
- Worked exampleFind the 2027 prediction when a graph climbs steadily by about 12 each year from 180 in 2024.
- Common mistakeWhy doesn't ice cream selling well alongside high drowning rates mean one causes the other?
- Going furtherWhat happens to a trend line when one wildly different data point joins the set?
Your turneasy1 of 3
A graph starts at 224 in 2024 and climbs steadily by about 17 each year. What value does the trend predict for 2027?Simple Probability
- How it worksHow does probability become wanted outcomes divided by total equally likely outcomes?
- Worked exampleFind the probability of drawing a red marble from a bag holding 4 red, 5 blue and 3 green.
- Worked exampleFind the probability of rolling a number greater than 4 on one six-sided die.
- Common mistakeWhy doesn't a coin that landed heads five times in a row become more likely to show tails?
- Going furtherWhat happens to a probability when you switch to asking for the chance it does not happen?
Your turnmedium1 of 3
A bag holds 8 red marbles, 9 blue and 9 green. Find the probability of drawing a red one. Round to three decimal places.Counting Outcomes and Probability Trees
- How it worksHow does a tree diagram branch once for every choice, with each path becoming an outcome?
- How it worksHow do you multiply along a branch of a probability tree to get that path's chance?
- Worked exampleFind how many different outcomes three coin flips can produce, using a tree.
- Worked exampleFind the probability of getting heads twice in a row on two fair coin flips.
- Ties togetherHow do probability trees, percents and frequency tables all describe the same counted data?
Your turneasy1 of 3
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