Core Academic Skills Assessment Mathematics: Data and Statistics Questions and Answers — Questions and Answers
Question 1: A teacher is analyzing the scores for a recent test: {85, 90, 88, 92, 86, 94, 32}. Which measure of central tendency would be most affected by the score of 32?
- Mode
- Median
- Mean (Correct answer)
- Range
Correct answer: Mean
The mean is calculated by summing all values and dividing by the count of values. An outlier, a value significantly different from others like the score of 32, will heavily skew the sum and therefore the mean. The median is the middle value and is less affected, while the mode is the most frequent value, and the range is a measure of spread, not central tendency.
Question 2: A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is drawn at random, what is the probability that it will be blue?
- 1/3
- 3/10 (Correct answer)
- 3/7
- 7/10
Correct answer: 3/10
The total number of marbles in the bag is 5 (red) + 3 (blue) + 2 (green) = 10 marbles. The number of favorable outcomes (drawing a blue marble) is 3. Therefore, the probability is the ratio of favorable outcomes to the total number of outcomes, which is 3/10.
Question 3: A student's scores on five history exams were 88, 95, 76, 88, and 83. What is the median score?
- 88 (Correct answer)
- 86
- 19
- 83
Correct answer: 88
To find the median, the scores must first be arranged in numerical order: 76, 83, 88, 88, 95. The median is the middle value in the ordered set. In this set of five scores, the middle value is the third one, which is 88.
Question 4: The bar chart below shows the number of books read by four students over the summer. Amy read 12, Ben read 8, Chloe read 15, and David read 9. How many more books did the student who read the most read than the student who read the least?
- 3
- 6
- 7 (Correct answer)
- 4
Correct answer: 7
First, identify the highest and lowest values from the data. The highest number of books read is 15 (by Chloe), and the lowest is 8 (by Ben). The question asks for the difference between these two values. 15 - 8 = 7.
Question 5: A researcher wants to survey the opinions of students at a large university with 20,000 students. Which of the following methods would produce the most representative random sample?
- Surveying the first 200 students who enter the library on a Monday morning.
- Asking for volunteers by posting flyers around the student union.
- Surveying all students in a single advanced-level biology course.
- Using a computer to randomly select 200 student ID numbers from the university's official roster. (Correct answer)
Correct answer: Using a computer to randomly select 200 student ID numbers from the university's official roster.
A representative random sample requires that every individual in the population has an equal chance of being selected. Using a computer to randomly select from a complete roster of all students achieves this. The other options introduce bias: surveying at the library over-represents students who use the library, volunteers are not a random group, and a single advanced class is not representative of the entire student body.
Question 6: What is the range of the following dataset representing the daily high temperatures (°F) for a week: {68, 72, 75, 65, 78, 71, 62}?
- 78
- 16 (Correct answer)
- 70.1
- 13
Correct answer: 16
The range is the difference between the highest and lowest values in a dataset. The highest temperature is 78°F, and the lowest is 62°F. The range is calculated as 78 - 62 = 16.
Core Academic Skills Assessment Mathematics: Data and Statistics Questions and Answers
A teacher is analyzing the scores for a recent test: {85, 90, 88, 92, 86, 94, 32}.
Which measure of central tendency would be most affected by the score of 32?