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Review statistics and probability for the ACT.
Learn step-by-step with practice exercises built right in.
The test scores for 5 students are: 72, 85, 90, 78, and 85. What is the mean score?
A) 78 B) 82 C) 85 D) 90 E) 410
The mean (average) is the sum of all values divided by the number of values.
Step 1: Add all scores 72 + 85 + 90 + 78 + 85 = 410
Step 2: Divide by number of students Mean = 410 ÷ 5 = 82
Answer: B) 82
Note: E) 410 is the sum, not the mean. This is a common trap answer!
Mean vs. Median vs. Mode: • Mean: Average (sum ÷ count) • Median: Middle value when arranged in order • Mode: Most frequent value
For this data: • Mean = 82 • Median = 85 (middle of 72, 78, 85, 85, 90) • Mode = 85 (appears twice)
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Explore more ACT Prep topics
Middle value in ordered data.
Most frequent value.
ACT Tip: Statistics problems are usually straightforward. Read carefully and look at the data provided.
A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. If one marble is randomly selected, what is the probability it is NOT blue?
F) 1/10 G) 1/5 H) 1/2 J) 3/5 K) 7/10
Probability = (Number of favorable outcomes) / (Total outcomes)
Step 1: Find total marbles 3 red + 5 blue + 2 green = 10 total
Step 2: Find marbles that are NOT blue Red + Green = 3 + 2 = 5 marbles
Step 3: Calculate probability P(not blue) = 5/10 = 1/2
Answer: H) 1/2
Alternative method (complement): P(not blue) = 1 - P(blue) P(blue) = 5/10 = 1/2 P(not blue) = 1 - 1/2 = 1/2 ✓
ACT Tip: For "NOT" probability, you can:
The heights (in inches) of 7 basketball players are: 70, 72, 73, 75, 76, 78, 80. What is the interquartile range (IQR)?
A) 3 B) 4 C) 6 D) 8 E) 10
The interquartile range (IQR) = Q3 - Q1
Data: 70, 72, 73, 75, 76, 78, 80 (already ordered, n = 7)
Step 1: Find the median (Q2) Middle value = 75 (4th value)
Step 2: Find Q1 (median of lower half) Lower half: 70, 72, 73 Q1 = 72 (middle of lower half)
Step 3: Find Q3 (median of upper half) Upper half: 76, 78, 80 Q3 = 78 (middle of upper half)
Step 4: Calculate IQR IQR = Q3 - Q1 = 78 - 72 = 6
Answer: C) 6
Why IQR matters: • Measures spread of middle 50% of data • Not affected by outliers (unlike range) • Used in box plots
Quartile Review: • Q1 = 25th percentile (1st quartile) • Q2 = 50th percentile (median) • Q3 = 75th percentile (3rd quartile) • IQR = Q3 - Q1 (middle 50%) • Range = Max - Min (entire spread)