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

In a circle (pie) graph, what does the whole circle represent and how many degrees does it contain?

The whole circle represents the total (100%) of the data, and it contains $360^{\circ}$.

How do you convert a percentage in a pie chart into the degree measure of its sector?

Multiply the percentage (as a decimal) by $360^{\circ}$: $\text{degrees} = \text{percent} \times 360^{\circ}$.

A sector of a pie chart has a central angle of $90^{\circ}$. What percentage of the total does it represent?

$\frac{90}{360} = \frac{1}{4} = 25\%$.

A pie chart shows that 40% of 200 students chose soccer. How many students is that?

$0.40 \times 200 = 80$ students.

In a pie chart, what must the sum of all the sector percentages equal?

All sectors must sum to 100% (and their central angles must sum to $360^{\circ}$).

What is a pictograph, and what does a key (legend) tell you?

A pictograph uses repeated symbols/icons to represent data. The key tells you how many units each symbol stands for, so you multiply the number of symbols by the key value.

In a pictograph, each book icon represents 5 books. A row shows 3.5 icons. How many books is that?

$3.5 \times 5 = 17.5$ books.

What is the purpose of a frequency table?

A frequency table lists each value or category alongside how many times it occurs (its frequency), organizing data so totals and patterns are easy to read.

How do you read a stem-and-leaf plot value like stem $3$ and leaf $7$?

The stem is the leading digit(s) and the leaf is the final digit, so stem $3$ and leaf $7$ represent the number $37$.

In a stem-and-leaf plot, how do you find the total number of data values?

Count all the leaves across every stem; each leaf represents one data value.

How can you find the mode quickly from a stem-and-leaf plot?

Look for a leaf digit that repeats within a single stem; the value occurring most often is the mode.

In a frequency table, how do you compute the mean?

Multiply each value by its frequency, sum those products, then divide by the total frequency: $\text{mean} = \frac{\sum (x \cdot f)}{\sum f}$.

What is the basic formula for the probability of a single event?

$P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of equally likely outcomes}}$.

What is the range of possible values for any probability?

A probability is always between 0 and 1 inclusive: $0 \leq P \leq 1$. A probability of 0 means impossible; 1 means certain.

What is the probability of rolling a 4 on a fair six-sided die?

$P(4) = \frac{1}{6}$, since there is 1 favorable outcome out of 6 equally likely outcomes.

A bag has 3 red, 2 blue, and 5 green marbles. What is the probability of drawing a blue marble?

$P(\text{blue}) = \frac{2}{3+2+5} = \frac{2}{10} = \frac{1}{5}$.

What does it mean for two events to be independent?

Two events are independent if the occurrence of one does not affect the probability of the other (e.g., separate coin flips or die rolls).

What is the multiplication rule for the probability of two independent events both occurring?

$P(A \text{ and } B) = P(A) \times P(B)$.

What is the probability of flipping two coins and getting heads on both?

$P(\text{HH}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$.

What is the probability of rolling a die and getting a 6, then flipping a coin and getting tails?

$\frac{1}{6} \times \frac{1}{2} = \frac{1}{12}$ (independent events multiplied).

What is a compound event in probability?

A compound event involves two or more simple events combined, such as 'A and B' or 'A or B' occurring together or in sequence.

For mutually exclusive events, what is the addition rule for $P(A \text{ or } B)$?

If A and B cannot happen at the same time, $P(A \text{ or } B) = P(A) + P(B)$.

What is the counting (fundamental) principle?

If one event can happen in $m$ ways and a second in $n$ ways, then the two together can happen in $m \times n$ ways. Multiply the number of choices for each stage.

Using the counting principle, how many outfits can you make from 4 shirts and 3 pairs of pants?

$4 \times 3 = 12$ outfits.

A meal has 3 appetizers, 5 entrees, and 2 desserts. How many different meals are possible?

$3 \times 5 \times 2 = 30$ meals.

How many two-digit codes can be formed using digits 0-9 if digits may repeat?

$10 \times 10 = 100$ codes.

What are complementary events, and what do their probabilities sum to?

Complementary events are an event and its opposite ('not the event'). Their probabilities sum to 1: $P(A) + P(\text{not } A) = 1$.

If the probability of rain is $0.3$, what is the probability it does NOT rain?

$P(\text{no rain}) = 1 - 0.3 = 0.7$ (the complement).

How are odds in favor of an event defined in terms of outcomes?

Odds in favor $= \frac{\text{favorable outcomes}}{\text{unfavorable outcomes}}$, written as favorable : unfavorable.

If the probability of an event is $\frac{2}{5}$, what are the odds in favor of it?

Favorable : unfavorable $= 2 : (5-2) = 2 : 3$.