Data and Statistics — Pre-Algebra Unit 10 practice.
This unit covers mean median mode, bar graphs and stem-and-leaf plots — essential concepts for Pre-Algebra. Use our interactive study games to test your understanding, or review questions in traditional format below.
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This unit covers mean median mode, bar graphs and stem-and-leaf plots — essential concepts for Pre-Algebra. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Mean, Median, and Mode
Mean is the average (sum divided by count), median is the middle value when data is ordered, and mode is the most frequently occurring value. Students must know when each measure is most appropriate and how to calculate all three from a data set. Exams often test the effect of adding, removing, or changing a value on each measure.
Key Points
- To find the median of an even-numbered data set, average the two middle values
- A data set can have no mode, one mode, or multiple modes
- The mean is sensitive to outliers; the median is not
- Always sort the data before finding the median
Data set: 4, 7, 2, 9, 7, 3. Find the mean, median, and mode.
First sort the data: 2, 3, 4, 7, 7, 9. Mean = (2+3+4+7+7+9) ÷ 6 = 32 ÷ 6 ≈ 5.3. Median = average of 3rd and 4th values = (4+7) ÷ 2 = 5.5. Mode = 7, because it appears twice and no other value repeats.
2 Bar Graphs
Bar graphs display categorical data using rectangular bars whose heights or lengths represent quantities. Students must be able to read values from a bar graph, compare bars, and interpret the scale on the axis. Exams also test the ability to identify the category with the greatest or least value and calculate differences between bars.
Key Points
- The vertical axis (y-axis) shows frequency or quantity; the horizontal axis (x-axis) shows categories
- Always check the scale — axis intervals may skip by 2, 5, 10, etc.
- A double bar graph compares two groups side by side using different colors or patterns
- To find the difference between two categories, subtract their bar heights
A bar graph shows book sales: Fiction = 45, Non-Fiction = 30, Mystery = 60. How many more Mystery books were sold than Non-Fiction?
Read the bar height for Mystery (60) and Non-Fiction (30) from the graph. Subtract the smaller value from the larger: 60 − 30 = 30. Mystery outsold Non-Fiction by 30 books.
3 Stem-and-Leaf Plots
A stem-and-leaf plot organizes numerical data by splitting each value into a stem (leading digit(s)) and a leaf (last digit), preserving the original data while showing its distribution. Students must be able to read individual values, find the mean, median, mode, and range from a stem-and-leaf plot. Back-to-back stem-and-leaf plots compare two data sets and are a common exam variation.
Key Points
- The stem is typically the tens digit; the leaf is the ones digit (e.g., 34 → stem 3, leaf 4)
- Leaves are always listed in order from least to greatest
- To find the range, subtract the smallest value (first leaf on first stem) from the largest (last leaf on last stem)
- Each leaf represents one individual data value — count leaves to find total number of values
Stem | Leaves 2 | 1 4 8 3 | 0 3 3 7 4 | 2 5 What is the median and range of this data?
The plot contains 9 values: 21, 24, 28, 30, 33, 33, 37, 42, 45. The median is the 5th value in order, which is 33. The range = largest − smallest = 45 − 21 = 24.
Questions, answered.
What is Data and Statistics?
Data and Statistics is Unit 10 of Pre-Algebra, covering mean median mode, bar graphs and stem-and-leaf plots.
How to study for Pre-Algebra Unit 10?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 25+ review questions across 5 different game modes.