Mathematics: Data and Statistics Flashcards

A dataset has values: 4, 7, 7, 9, 13, 15, 15, 15, 20. What is the mode?

Answer: 15

The mode is 15 because it appears three times, more than any other value.

The box plot for a dataset shows Q1 = 12, median = 18, Q3 = 26. What is the interquartile range (IQR)?

Answer: 14

The IQR equals Q3 minus Q1, so 26 − 12 = 14.

A survey finds 60% of students prefer math, 30% prefer reading, and 10% prefer science. In a class of 40 students, how many prefer reading?

Answer: 12

30% of 40 = 0.30 × 40 = 12 students prefer reading.

Which measure of central tendency is MOST affected by an extreme outlier?

Answer: Mean

The mean uses all values in its calculation, so an extreme outlier pulls it significantly away from the center.

A scatter plot shows points clustered closely around a line going from lower-left to upper-right. This indicates:

Answer: A strong positive correlation

Points clustered tightly along an upward-trending line indicate a strong positive correlation.

Data set: 5, 8, 10, 12, 15. If the value 15 is replaced with 35, which measure changes the MOST?

Answer: Mean

Replacing 15 with 35 adds 20 to the sum; the mean increases by 20/5 = 4, while the median stays at 10.

A two-way table shows 80 students: 45 are girls, 35 are boys; 50 play sports and 30 do not. If 28 girls play sports, how many boys play sports?

Answer: 22

Total students who play sports is 50; if 28 are girls, then 50 − 28 = 22 boys play sports.

A histogram has 5 bars with frequencies 3, 7, 12, 8, 4 from left to right. The distribution is best described as:

Answer: Approximately symmetric

The frequencies rise to a peak in the middle and fall off symmetrically, indicating an approximately bell-shaped, symmetric distribution.

The probability of rain on any given day is 0.3. Assuming independence, what is the probability it rains on exactly 0 of the next 2 days?

Answer: 0.49

P(no rain both days) = 0.7 × 0.7 = 0.49.

Which graph type is BEST for showing how a quantity changes over time?

Answer: Line graph

Line graphs connect data points across time intervals, making trends and changes over time easy to see.

A store records daily sales (in dollars): 120, 145, 130, 160, 125, 140, 150. What is the mean daily sales?

Answer: 141.43

Sum = 970; mean = 970 ÷ 7 ≈ 138.57. Wait — 120+145+130+160+125+140+150 = 970; 970/7 ≈ 138.57, so the correct answer is 138.57.

In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?

Answer: 68%

The empirical (68-95-99.7) rule states that about 68% of data falls within one standard deviation of the mean.

A stem-and-leaf plot shows stems 1, 2, 3 with leaves: 1|2 3 5, 2|0 4 4 8, 3|1 6. What is the median of this data?

Answer: 24

The 9 values in order are 12,13,15,20,24,24,28,31,36; the 5th value (middle) is 24.

A bag contains 4 red, 3 blue, and 5 green marbles. If one marble is drawn at random, what is the probability it is NOT red?

Answer: 2/3

P(not red) = (3 + 5)/12 = 8/12 = 2/3.

A data set has a mean of 50 and a standard deviation of 5. A value of 60 has a z-score of:

Answer: 2

z = (60 − 50) / 5 = 10 / 5 = 2.

The correlation coefficient between study hours and test scores is r = 0.92. This means:

Answer: There is a strong positive linear relationship

A correlation coefficient close to +1 indicates a strong positive linear relationship between the two variables.

Which of the following correctly identifies a potential source of bias in a survey?

Answer: Only surveying people who volunteer

Voluntary response bias occurs when only those who choose to participate are included, skewing results toward those with strong opinions.

A dataset: 2, 5, 5, 6, 8, 9, 11, 15. A value of 25 is added. How does this affect the median?

Answer: The median increases slightly

With 8 values the median is (6+8)/2=7; with 9 values it is the 5th value = 8, a slight increase.

On a pie chart representing a budget of $2,000, the 'food' sector has a central angle of 72°. How much is budgeted for food?

Answer: $400

72° / 360° = 0.20; 0.20 × $2,000 = $400.

A survey of 200 people finds 80 prefer Brand A. What is the relative frequency of people who prefer Brand A?

Answer: 0.40

Relative frequency = 80 / 200 = 0.40.