Core Academic Skills Assessment Mathematics: Data and Statistics — Questions and Answers

Question 1: A dataset has values: 4, 7, 7, 9, 13, 15, 15, 15, 20. What is the mode?

7
9
13
15 (Correct answer)

Correct answer: 15

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

Question 2: The box plot for a dataset shows Q1 = 12, median = 18, Q3 = 26. What is the interquartile range (IQR)?

6
8
14 (Correct answer)
18

Correct answer: 14

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

Question 3: 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?

4
10
12 (Correct answer)
24

Correct answer: 12

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

Question 4: Which measure of central tendency is MOST affected by an extreme outlier?

Median
Mode
Mean (Correct answer)
Range

Correct answer: Mean

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

Question 5: A scatter plot shows points clustered closely around a line going from lower-left to upper-right. This indicates:

No correlation
A strong negative correlation
A strong positive correlation (Correct answer)
A weak positive correlation

Correct answer: A strong positive correlation

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

Question 6: Data set: 5, 8, 10, 12, 15. If the value 15 is replaced with 35, which measure changes the MOST?

Median
Mode
Mean (Correct answer)
Lower quartile

Correct answer: Mean

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

Question 7: 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?

17
22 (Correct answer)
28
30

Correct answer: 22

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

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

Skewed right
Uniform
Approximately symmetric (Correct answer)
Skewed left

Correct answer: Approximately symmetric

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

Question 9: 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?

0.09
0.21
0.42
0.49 (Correct answer)

Correct answer: 0.49

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

Question 10: Which graph type is BEST for showing how a quantity changes over time?

Pie chart
Bar graph
Line graph (Correct answer)
Stem-and-leaf plot

Correct answer: Line graph

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

Question 11: A store records daily sales (in dollars): 120, 145, 130, 160, 125, 140, 150. What is the mean daily sales?

138.57
140.00
141.43 (Correct answer)
145.00

Correct 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.

Question 12: In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?

50%
68% (Correct answer)
95%
99.7%

Correct answer: 68%

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

Question 13: 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?

20
24 (Correct answer)
24.5
28

Correct answer: 24

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

Question 14: 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?

1/3
5/12
2/3 (Correct answer)
4/12

Correct answer: 2/3

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

Question 15: A data set has a mean of 50 and a standard deviation of 5. A value of 60 has a z-score of:

1
2 (Correct answer)
5
10

Correct answer: 2

z = (60 − 50) / 5 = 10 / 5 = 2.

Question 16: The correlation coefficient between study hours and test scores is r = 0.92. This means:

Study hours cause higher scores
There is a strong positive linear relationship (Correct answer)
92% of students studied
The data has 92 points

Correct answer: There is a strong positive linear relationship

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

Question 17: Which of the following correctly identifies a potential source of bias in a survey?

Using a large sample size
Randomly selecting respondents
Only surveying people who volunteer (Correct answer)
Including multiple answer choices

Correct 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.

Question 18: A dataset: 2, 5, 5, 6, 8, 9, 11, 15. A value of 25 is added. How does this affect the median?

The median increases by about 8.5
The median stays the same
The median increases slightly (Correct answer)
The median decreases

Correct 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.

Question 19: 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?

$200
$360
$400 (Correct answer)
$720

Correct answer: $400

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

Question 20: A survey of 200 people finds 80 prefer Brand A. What is the relative frequency of people who prefer Brand A?

0.30
0.40 (Correct answer)
0.45
0.80

Correct answer: 0.40

Relative frequency = 80 / 200 = 0.40.

Question 21: Two events A and B are mutually exclusive. P(A) = 0.4 and P(B) = 0.25. What is P(A or B)?

0.10
0.15
0.65 (Correct answer)
0.75

Correct answer: 0.65

For mutually exclusive events, P(A or B) = P(A) + P(B) = 0.4 + 0.25 = 0.65.

Core Academic Skills Assessment Mathematics: Data and Statistics

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

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