California High School Proficiency Examination (CHSPE) Mathematics: Data Analysis, Statistics, and Probability Syllabus

Mathematics: Data Analysis, Statistics, and Probability syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics: Data Analysis, Statistics, and Probability in California High School Proficiency Examination (CHSPE), not a summary of it.

1. 1

   Interpreting Data Displays

   3 topics

   • Reading Tables and Charts
     • Extracting values from data tables
     • Comparing categories
   • Graphs and Plots
     • Bar graphs and line graphs
     • Circle graphs and pictographs
   • Drawing Conclusions from Data
     • Identifying trends
     • Detecting misleading displays
2. 2

   Measures of Central Tendency and Spread

   3 topics

   • Mean, Median, and Mode
     • Computing each measure
     • Choosing the best measure for a data set
   • Range and Variation
     • Finding the range
     • Interpreting spread
   • Effects of Data Changes
     • How outliers affect the mean
     • Comparing data sets
3. 3

   Probability

   3 topics

   • Basic Probability Concepts
     • Theoretical probability of simple events
     • Expressing probability as fractions, decimals, and percents
   • Compound and Combined Events
     • Independent and dependent events
     • Counting outcomes with tree diagrams
   • Experimental Probability and Predictions
     • Relative frequency from experiments
     • Making predictions from samples

Mathematics: Data Analysis, Statistics, and Probability flashcards for California High School Proficiency Examination (CHSPE)

25 of 50 cards from the Mathematics: Data Analysis, Statistics, and Probability deck — real questions with worked answers.

1. When reading a data table, what do the rows and columns represent?

   Columns are vertical and usually label the categories or variables; rows are horizontal and contain the individual data entries. You find a value by locating where a specific row and column intersect.

2. In a table or chart, what is a 'key' or 'legend' used for?

   It explains what the symbols, colors, or labels in the chart stand for, so you can correctly interpret each part of the data display.

3. What is the difference between a frequency table and a regular data table?

   A frequency table shows how many times (the count or frequency) each value or category occurs, while a regular data table simply lists data values without necessarily counting repetitions.

4. What type of graph is best for showing parts of a whole as percentages?

   A circle graph (pie chart), because each sector represents a fraction of the total and all sectors together equal 100%.

5. What type of graph is best for showing change over time?

   A line graph, because it connects data points to show trends and how values rise or fall across time intervals.

6. What type of graph is best for comparing amounts across distinct categories?

   A bar graph, because the height (or length) of each bar shows the value for each separate category, making comparison easy.

7. What does a scatter plot show?

   It shows the relationship (correlation) between two variables by plotting ordered pairs as points; the pattern of points reveals whether the variables are positively, negatively, or not correlated.

8. On a scatter plot, what does a positive correlation look like?

   The points trend upward from left to right, meaning as one variable increases the other also tends to increase.

9. On a scatter plot, what does a negative correlation look like?

   The points trend downward from left to right, meaning as one variable increases the other tends to decrease.

10. What information does a stem-and-leaf plot preserve that a histogram does not?

    A stem-and-leaf plot keeps the actual individual data values (the leaves), while a histogram only shows the count in each interval and loses the original values.

11. How does a histogram differ from a bar graph?

    A histogram displays the frequency of data within continuous numerical intervals (bars touch), while a bar graph compares separate categories (bars have gaps between them).

12. In a box-and-whisker plot, what five values are shown?

    The minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum — the five-number summary.

13. What does the 'box' in a box-and-whisker plot represent?

    The box spans from Q1 to Q3, representing the interquartile range (IQR), which contains the middle 50% of the data.

14. What does it mean to interpolate from a graph?

    To estimate a value that falls between known data points already shown on the graph.

15. What does it mean to extrapolate from a graph?

    To estimate or predict a value beyond the range of the known data points by extending the observed trend.

16. When drawing conclusions from data, why must you check the scale on an axis?

    Because a misleading or non-zero/uneven scale can exaggerate or minimize differences, leading to incorrect conclusions about the data.

17. What is the difference between correlation and causation?

    Correlation means two variables move together in a pattern; causation means one variable directly causes a change in the other. Correlation does not prove causation.

18. What is a valid conclusion versus an assumption when interpreting data?

    A valid conclusion is supported directly by the data shown; an assumption goes beyond the data and is not actually proven by it.

19. How do you calculate the mean (average) of a data set?

    Add all the values together, then divide the sum by the number of values.

20. How do you find the median of a data set?

    Arrange the values in numerical order, then take the middle value. If there is an even number of values, average the two middle values.

21. What is the mode of a data set?

    The value that appears most frequently. A data set can have no mode, one mode, or more than one mode.

22. Which measure of central tendency is most affected by outliers (extreme values)?

    The mean, because every value is included in its calculation, so an extreme value pulls the mean toward it.

23. Which measure of central tendency is best to use when a data set has outliers?

    The median, because it depends only on the middle position and is not distorted by extreme values.

24. Find the mean, median, and mode of: 4, 8, 8, 10, 20.

    Mean = (4+8+8+10+20)/5 = 50/5 = 10; Median = 8 (middle value); Mode = 8 (appears most often).

25. What is the term for the average value of a data set, and what symbol often represents it?

    The mean (arithmetic average), often represented by x̄ (x-bar).

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