SSAT (Secondary School Admission Test) Quantitative Reasoning: Data Analysis and Probability Syllabus

Quantitative Reasoning: Data Analysis 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 Quantitative Reasoning: Data Analysis and Probability in SSAT (Secondary School Admission Test), not a summary of it.

1. 1

   Statistics and Measures of Center

   3 topics

   • Mean, median, and mode
     • Finding a missing value given the mean
     • Effect of outliers on center
   • Range and spread
   • Weighted averages
2. 2

   Interpreting Data Displays

   4 topics

   • Reading bar graphs and line graphs
   • Circle (pie) graphs and percentages
   • Tables and pictographs
   • Stem-and-leaf plots and frequency tables
3. 3

   Counting and Probability

   4 topics

   • Basic probability of single events
     • Theoretical versus experimental probability
   • Probability of compound and independent events
   • The counting principle
   • Complementary events and odds

Quantitative Reasoning: Data Analysis and Probability flashcards for SSAT (Secondary School Admission Test)

19 of 50 cards from the Quantitative Reasoning: Data Analysis and Probability deck — real questions with worked answers.

1. What is the mean (arithmetic average) of a data set, and how do you calculate it?

   The mean is the sum of all values divided by the number of values: $\text{mean} = \frac{\text{sum of values}}{\text{number of values}}$.

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

   Arrange the values in order. If there is an odd number of values, the median is the middle one. If even, the median is the average of the two middle values.

3. What is the mode of a data set?

   The mode is the value that appears most frequently. A set can have no mode, one mode, or multiple modes (bimodal/multimodal).

4. Find the median of $4, 8, 15, 16, 23, 42$.

   There are 6 values (even), so average the two middle ones: $\frac{15+16}{2} = \frac{31}{2} = 15.5$.

5. What is the mean of $3, 7, 7, 19$?

   $\frac{3+7+7+19}{4} = \frac{36}{4} = 9$.

6. Which measure of central tendency is most affected by an extreme outlier, and why?

   The mean, because it uses every value in its sum, so a single very large or very small value shifts it noticeably. The median is resistant to outliers.

7. If a data set is $5, 5, 6, 7, 100$, which is larger, the mean or the median?

   The mean is larger. Mean $= \frac{123}{5} = 24.6$; median $= 6$. The outlier 100 pulls the mean up.

8. What is the range of a data set, and how is it calculated?

   The range is a measure of spread equal to the largest value minus the smallest value: $\text{range} = \text{max} - \text{min}$.

9. Find the range of $12, 7, 25, 19, 4$.

   $\text{range} = 25 - 4 = 21$.

10. Does the range tell you anything about values between the maximum and minimum?

    No. The range only measures total spread (max minus min); it ignores how the middle values are distributed.

11. What does it mean for one data set to have a greater spread than another?

    It means its values are more dispersed (farther apart), typically shown by a larger range, so the data is less clustered around the center.

12. What is a weighted average, and when is it used?

    A weighted average accounts for items counting different amounts (weights). It is used when some values represent more items than others, such as combining group sizes or grade categories.

13. What is the formula for a weighted average?

    $\text{weighted average} = \frac{\sum (\text{value} \times \text{weight})}{\sum \text{weights}}$.

14. A class of 10 students averages 80 and a class of 20 students averages 95. What is the combined (weighted) average?

    $\frac{10(80) + 20(95)}{10+20} = \frac{800 + 1900}{30} = \frac{2700}{30} = 90$.

15. Why can't you simply average two group averages directly to get the overall average?

    Because the groups may have different sizes. You must weight each average by its group size; only when the groups are equal in size does a plain average work.

16. A student's grade is 30% homework (score 90) and 70% exams (score 80). What is the weighted grade?

    $0.30(90) + 0.70(80) = 27 + 56 = 83$.

17. On a bar graph, what does the height (or length) of each bar represent?

    The height/length of each bar represents the value or frequency of that category; taller bars indicate larger values.

18. What is the key visual difference between a bar graph and a line graph?

    A bar graph uses separate bars to compare distinct categories, while a line graph connects points to show how a value changes continuously, usually over time (trends).

19. When reading a line graph, what does an upward-sloping segment indicate?

    An upward (rising) segment indicates the value is increasing over that interval; a downward segment indicates a decrease, and a flat segment indicates no change.

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