بنك الأسئلة
Data & Statistics Questions.
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A recipe calls for 3 cups of flour to make 12 cookies. How many cups are needed to make 36 cookies?
- 6
- 8
- 9 ✓
- 12
الشرح
36/12 = 3, so multiply by 3: 3 × 3 = 9 cups.
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A car travels 240 miles in 4 hours. At the same rate, how far does it travel in 7 hours?
- 300
- 360
- 420 ✓
- 480
الشرح
Rate = 240/4 = 60 mph. Distance = 60 × 7 = 420 miles.
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A map uses a scale of 1 inch = 25 miles. Two cities are 3.5 inches apart on the map. What is the actual distance?
- 75 miles
- 82.5 miles
- 87.5 miles ✓
- 90 miles
الشرح
3.5 × 25 = 87.5 miles.
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A store sells juice in 12 oz bottles for $2.40 or 20 oz bottles for $3.60. Which size is the better value, and by how much per ounce?
- 12 oz, by $0.02 per oz
- 20 oz, by $0.01 per oz
- 20 oz, by $0.02 per oz ✓
- Same value per ounce
الشرح
12 oz: $2.40/12 = $0.20/oz. 20 oz: $3.60/20 = $0.18/oz. The 20 oz bottle is better by $0.02/oz.
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A shirt costs $40 and is on sale for 25% off. What is the sale price?
- $25
- $28
- $30 ✓
- $32
الشرح
Discount = 25% of $40 = $10. Sale price = $40 − $10 = $30.
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A TV was originally $500 and is now $425. What is the percent decrease?
- 10%
- 12%
- 15% ✓
- 17%
الشرح
Percent decrease = (500 − 425)/500 × 100 = 75/500 × 100 = 15%.
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A student scored 78 out of 120 points. What percent did she score?
- 60%
- 62%
- 65% ✓
- 70%
الشرح
78/120 × 100 = 65%.
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After a 20% increase, a price is $84. What was the original price?
- $60
- $65
- $70 ✓
- $75
الشرح
Original × 1.20 = 84 → Original = 84/1.20 = $70.
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A bag contains 5 red, 3 blue, and 2 green marbles. What is the probability of drawing a blue marble?
- 1/5
- 3/10 ✓
- 1/2
- 3/5
الشرح
P(blue) = 3/10.
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One card is drawn from a standard 52-card deck. What is the probability of drawing a face card (J, Q, or K)?
- 1/13
- 3/13 ✓
- 4/13
- 1/4
الشرح
There are 12 face cards in a deck of 52. P = 12/52 = 3/13.
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A class of 40 students includes 15 boys who like math, 5 boys who do not, 10 girls who like math, and 10 girls who do not. What is the probability that a randomly chosen student is a girl who likes math?
- 1/5
- 1/4 ✓
- 1/2
- 10/15
الشرح
10 girls who like math out of 40 students: P = 10/40 = 1/4.
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P(A) = 0.4 and P(B) = 0.3. If A and B are independent events, what is P(A and B)?
- 0.07
- 0.10
- 0.12 ✓
- 0.70
الشرح
For independent events: P(A and B) = P(A) × P(B) = 0.4 × 0.3 = 0.12.
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The data set is 4, 7, 7, 9, 13. What is the median?
- 7 ✓
- 8
- 9
- 10
الشرح
The data is already in order. The middle value (3rd of 5) is 7.
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The data set is 2, 5, 7, 8, 8, 10. What is the mean?
- 6.5
- 6.67 ✓
- 7
- 8
الشرح
Sum = 2 + 5 + 7 + 8 + 8 + 10 = 40. Mean = 40/6 ≈ 6.67.
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Which measure of center is most affected by an extreme outlier?
- Mean ✓
- Median
- Mode
- Range
الشرح
The mean uses all values in its calculation, so a very large or very small outlier pulls it significantly. The median is resistant to outliers.
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What does the standard deviation of a data set measure?
- The average value of the data
- The middle value of the data
- The most frequent value in the data
- The spread of data values around the mean ✓
الشرح
Standard deviation measures how much the data values vary from the mean — it quantifies spread.
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A bar chart shows January sales: 200, February: 150, March: 250. What is the total for these three months?
- 500
- 550
- 600 ✓
- 650
الشرح
200 + 150 + 250 = 600.
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A line of best fit for study hours (x) and test score (y) is y = 5x + 60. What score does the model predict for 8 hours of study?
- 80
- 90
- 95
- 100 ✓
الشرح
y = 5(8) + 60 = 40 + 60 = 100.
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A histogram shows 30% of 200 students scored 70–80, 45% scored 80–90, and 25% scored 90–100. How many students scored in the 80–90 range?
- 70
- 80
- 90 ✓
- 100
الشرح
45% of 200 = 0.45 × 200 = 90 students.
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A study finds a correlation coefficient of −0.85 between hours of sleep and reaction time. What does this indicate?
- No relationship
- Weak positive relationship
- Weak negative relationship
- Strong negative relationship ✓
الشرح
A value of −0.85 is close to −1, indicating a strong negative correlation: more sleep is associated with lower (faster) reaction times.
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A runner completes 5 laps in 20 minutes. How long does it take to complete 8 laps at the same pace?
- 28 min
- 30 min
- 32 min ✓
- 36 min
الشرح
Rate = 20/5 = 4 min per lap. Time for 8 laps = 8 × 4 = 32 minutes.
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A class has 12 boys and 18 girls. What is the ratio of boys to the total number of students?
- 2:3
- 2:5 ✓
- 3:5
- 3:2
الشرح
Total = 30. Ratio of boys to total = 12:30 = 2:5.
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A printer prints 240 pages in 6 minutes. How many pages does it print in 25 minutes?
- 800
- 900
- 1,000 ✓
- 1,200
الشرح
Rate = 240/6 = 40 pages/min. Pages in 25 min = 40 × 25 = 1,000.
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In a survey, 3 out of every 8 people prefer tea. In a group of 320 people, how many prefer tea?
- 100
- 110
- 120 ✓
- 130
الشرح
(3/8) × 320 = 120 people.
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Two workers can complete a job in 6 hours together. Worker A alone takes 10 hours. How long does Worker B alone take?
- 12 hours
- 15 hours ✓
- 18 hours
- 20 hours
الشرح
Combined rate = 1/6 jobs/hr. A's rate = 1/10. B's rate = 1/6 − 1/10 = 5/30 − 3/30 = 2/30 = 1/15. B alone takes 15 hours.
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A jacket costs $80. It is discounted by 15%. What is the discount amount?
- $10
- $12 ✓
- $14
- $16
الشرح
Discount = 15% of $80 = 0.15 × 80 = $12.
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A population grew from 4,000 to 4,500. What was the percent increase?
- 10%
- 11.1%
- 12.5% ✓
- 15%
الشرح
Percent increase = (500/4000) × 100 = 12.5%.
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An item is marked up 40% from its wholesale price, then discounted 20% at a sale. What is the overall percent change from the wholesale price?
- 8% decrease
- 8% increase
- 12% increase ✓
- 20% increase
الشرح
Let wholesale = 100. After 40% markup: 140. After 20% discount: 140 × 0.80 = 112. Net change = +12%.
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A bank account earns 5% simple interest per year. After how many years will an initial deposit of $600 grow to $750?
- 3
- 4
- 5 ✓
- 6
الشرح
Simple interest: I = Prt. 150 = 600 × 0.05 × t → t = 150/30 = 5 years.
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A price is reduced by 30%, then reduced by another 20%. What is the total percentage decrease from the original price?
- 44% ✓
- 50%
- 54%
- 56%
الشرح
Let original = 100. After 30% off: 70. After 20% off that: 70 × 0.80 = 56. Total decrease = 100 − 56 = 44%.
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A fair die is rolled once. What is the probability of rolling a number greater than 4?
- 1/6
- 1/3 ✓
- 1/2
- 2/3
الشرح
Numbers greater than 4 on a standard die: 5 and 6 — two outcomes. P = 2/6 = 1/3.
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A bag has 4 red, 5 blue, and 1 green marble. One marble is drawn and not replaced; then a second is drawn. What is the probability both are red?
- 4/25
- 2/15 ✓
- 4/10
- 1/5
الشرح
P(1st red) = 4/10. P(2nd red | 1st red) = 3/9. P(both red) = (4/10)(3/9) = 12/90 = 2/15.
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In a class of 30 students, 18 play sports and 12 do not. If two students are chosen at random, what is the probability both play sports?
- 51/145 ✓
- 9/25
- 3/5
- 18/30
الشرح
P = (18/30) × (17/29) = 306/870 = 51/145.
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A spinner has 8 equal sections numbered 1–8. What is the probability of spinning an even number or a number greater than 5?
- 5/8 ✓
- 6/8
- 7/8
- 1/2
الشرح
Evens: {2, 4, 6, 8}. Greater than 5: {6, 7, 8}. Union: {2, 4, 6, 7, 8} — 5 outcomes. P = 5/8.
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Events A and B are mutually exclusive. P(A) = 0.35 and P(B) = 0.25. What is P(A or B)?
- 0.0875
- 0.10
- 0.60 ✓
- 0.875
الشرح
For mutually exclusive events: P(A or B) = P(A) + P(B) = 0.35 + 0.25 = 0.60.
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The data set is 3, 5, 7, 7, 9, 11. What is the mode?
- 5
- 6
- 7 ✓
- 9
الشرح
The mode is the most frequently occurring value. 7 appears twice; all others appear once.
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The data set is 10, 14, 18, 22, 26. What is the interquartile range (IQR)?
- 8
- 10
- 12 ✓
- 16
الشرح
Q1 = 12 (midpoint of lower half: 10, 14), Q3 = 24 (midpoint of upper half: 22, 26). IQR = 24 − 12 = 12.
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Which of the following best describes a data distribution that is skewed right?
- The mean is less than the median
- The mean equals the median
- The mean is greater than the median ✓
- The mode is greater than the mean
الشرح
In a right-skewed (positively skewed) distribution, the long tail is on the right and the mean is pulled above the median by the high outliers.
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A data set has a mean of 50 and a standard deviation of 5. A new data point of 65 is added. Compared to the original set, the new mean will be ___.
- Higher, because 65 > 50 ✓
- Lower, because adding data decreases the mean
- Unchanged, because one point does not affect the mean
- The same as the median
الشرح
Adding a value (65) above the current mean (50) will pull the mean upward, so the new mean will be higher.
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A data set has values 4, 6, 8, 10, 12. If every value is multiplied by 3, what happens to the mean and standard deviation?
- Mean triples; standard deviation stays the same
- Mean triples; standard deviation triples ✓
- Mean stays the same; standard deviation triples
- Both stay the same
الشرح
Multiplying every value by a constant k multiplies both the mean and the standard deviation by k. So both triple.
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A pie chart shows that 35% of students prefer math, 25% prefer science, and 40% prefer English. In a class of 80 students, how many prefer math?
- 20
- 24
- 28 ✓
- 32
الشرح
35% of 80 = 0.35 × 80 = 28.
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A scatter plot shows that as x increases, y tends to decrease. Which best describes the correlation?
- Positive correlation
- Negative correlation ✓
- No correlation
- Perfect positive correlation
الشرح
When one variable increases and the other decreases, the correlation is negative.
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A two-way table shows: 40 students passed Math, 30 passed English, and 15 passed both. Using the inclusion-exclusion principle, how many passed at least one subject?
- 55 ✓
- 60
- 65
- 70
الشرح
P(Math or English) = 40 + 30 − 15 = 55.
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A survey of 200 people found that 120 own a car, 80 own a bike, and 40 own both. What percentage own neither?
- 10%
- 15%
- 20% ✓
- 25%
الشرح
Own at least one = 120 + 80 − 40 = 160. Own neither = 200 − 160 = 40. Percent = 40/200 × 100 = 20%.
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A line of best fit for a data set is y = −3x + 90, where x is the number of absences and y is the final grade. What does the slope −3 indicate?
- For each additional absence, the predicted grade increases by 3 points
- For each additional absence, the predicted grade decreases by 3 points ✓
- The predicted grade when there are 0 absences is −3
- The predicted grade when there are 0 absences is 3
الشرح
The slope represents the rate of change. A slope of −3 means each additional absence is associated with a 3-point decrease in the predicted grade.