Praxis Core Data Interpretation, Statistics, and Probability Summary

1. Sum: 10 + 15 + 9 + 22 + 16 = 72.
2. Mean: 72 ÷ 5 = 14.4.

Check: 14.4 × 5 = 72.

Wrong choices

• "15": 15 is the median (the middle value when ordered), not the mean.
• "18": This divides the total (72) by 4 instead of by 5 numbers.
• "13": 13 is the range (22 − 9), not the mean.
• "72": 72 is the total. It must be divided by how many numbers there are.

1. Order: 3, 4, 7, 8, 9, 12.
2. The two middle values are 7 and 8.
3. Median: (7 + 8) ÷ 2 = 7.5.

Check: three values (3, 4, 7) are below 7.5 and three (8, 9, 12) are above it.

Wrong choices

• "6.5": This takes the middle two numbers without first putting the list in order (9 and 4).
• "7": With six numbers there are two middle values (7 and 8); the median is their average.
• "8": This picks only one of the two middle values.
• "9": 9 is the range (12 − 3), not the median.

1. Total marbles: 4 + 6 + 5 = 15.
2. Blue: 6.
3. Probability: 6/15 = 2/5.

Check: 2/5 = 0.4, and 0.4 × 15 = 6 blue marbles.

Wrong choices

• "2/3": This compares blue to non-blue (6 to 9). Probability compares blue to ALL marbles (6 out of 15).
• "3/5": 3/5 is the probability of NOT picking blue.
• "1/3": This assumes the three colors are equally likely. There are more blue marbles than red or green.
• "1/6": This puts 1 over the number of blue marbles.

1. P(heads) = 1/2. P(6) = 1/6.
2. P(both) = 1/2 × 1/6 = 1/12.

Check: there are 2 × 6 = 12 equally likely pairs, and only one of them is (heads, 6).

Wrong choices

• "2/3": This adds 1/2 + 1/6. For two independent events that BOTH must happen, multiply.
• "7/12": 7/12 is the probability of heads OR a 6, not both.
• "1/8": This puts 1 over 2 + 6. The total number of outcomes is 2 × 6 = 12.
• "1/6": This gives only the chance of rolling a 6 and ignores the coin.

Count each value: 2 (once), 4 (twice), 5 (once), 7 (three times), 9 (once). The value 7 appears most often, so the mode is 7.

Check: no other value appears three or more times.

Wrong choices

• "4": 4 appears twice, but 7 appears three times.
• "6": 6 is the median ((5 + 7) ÷ 2), not the mode.
• "3": 3 is HOW MANY times the mode appears, not the mode itself.
• "5.625": 5.625 is the mean (45 ÷ 8), not the mode.

1. Greatest: 12. Least: −8.
2. Range: 12 − (−8) = 12 + 8 = 20°F.

Check: on a thermometer, going from −8 up to 0 is 8 degrees, and from 0 up to 12 is 12 more; 8 + 12 = 20.

Wrong choices

• "4°F": This subtracts 8 instead of −8. Subtracting a negative number means adding: 12 − (−8) = 20.
• "15°F": This uses −3 as the lowest value. The lowest temperature is −8°F.
• "5°F": 5°F is the median (the middle value), not the range.
• "2.6°F": 2.6°F is the mean (13 ÷ 5), not the range.

1. Jan → Feb: 3,800 − 4,200 = −400.
2. Feb → Mar: 5,100 − 3,800 = +1,300.
3. Mar → Apr: 4,600 − 5,100 = −500.
4. Apr → May: 5,700 − 4,600 = +1,100.

The largest increase is +1,300, from February to March.

Check: 3,800 + 1,300 = 5,100.

Wrong choices

• "April to May": Sales rose $1,100 from April to May, which is less than the $1,300 rise from February to March.
• "The two increases (February to March and April to May) were equal": The increases were $1,300 and $1,100, which are not equal.
• "March to April": Sales went DOWN $500 from March to April.
• "January to February": Sales went DOWN $400 from January to February.

1. Numbers greater than 4: 5 and 6, which is 2 outcomes.
2. Total outcomes: 6.
3. Probability: 2/6 = 1/3.

Check: the probability of 4 or less is 4/6, and 2/6 + 4/6 = 1.

Wrong choices

• "1/2": This counts 4, 5, and 6. "Greater than 4" does not include 4.
• "1/6": This counts only one number. Both 5 and 6 are greater than 4.
• "2/3": 2/3 is the probability of rolling 4 or less.
• "5/6": This counts every number except 4.

1. Class A total: 20 × 80 = 1,600.
2. Class B total: 30 × 70 = 2,100.
3. Combined mean: (1,600 + 2,100) ÷ 50 = 3,700 ÷ 50 = 74.

Check: 74 is closer to 70 than to 80, which makes sense because Class B is larger.

Wrong choices

• "75": This averages the two class means. Class B has more students, so it counts more.
• "76": This gives Class A the larger weight. Class B has 30 students, not 20.
• "70": This uses only the larger class.
• "3,700": 3,700 is the total of all scores. It must be divided by 50 students.

1. Total needed for five tests: 87 × 5 = 435.
2. Current total: 78 + 85 + 92 + 88 = 343.
3. Needed: 435 − 343 = 92.

Check: (343 + 92) ÷ 5 = 435 ÷ 5 = 87.

Wrong choices

• "87": Scoring 87 would not raise his current mean (85.75) all the way to 87.
• "88.25": This adds the 1.25-point shortfall to 87 once. The fifth test must make up 1.25 for each of the four earlier tests too.
• "85.75": 85.75 is his current mean, not the score he needs.
• "435": 435 is the total needed for all five tests, not the fifth score.