Free CLAST Statistics and Probability Questions and Answers — Questions and Answers
Question 1: A college president is curious about the most well-liked courses among students. The president makes the decision to poll a representative sample of students. Which method would be best for gathering a representative sample of college students from a statistically neutral perspective?
- Survey the first hundred students from an alphabetical listing
- Have students voluntarily mail in their preferences
- Survey a random sample of students from the English department
- Survey a random sample of students from a list of the entire student body (Correct answer)
Correct answer: Survey a random sample of students from a list of the entire student body
To obtain a statistically neutral and representative sample, every member of the population must have an equal chance of being selected. Surveying a random sample from a complete list of the entire student body ensures this randomness and avoids biases. Other methods, like surveying specific departments or using voluntary responses, would introduce sampling bias.
Question 2: The average number of school-age children per home in a city must be determined by the primary school board. The board decides to run a poll in order to achieve this. What process would be most suitable for choosing a statistically unbiased sample?
- Select the largest grocery store in the city and survey a random sample of its customers
- Survey a random sample of the people who work at a local medical center
- Survey all the residents of the largest subdivisions in the city
- Randomly select geographic regions of the city and then survey a random sample of people within the regions (Correct answer)
Correct answer: Randomly select geographic regions of the city and then survey a random sample of people within the regions
Randomly selecting geographic regions and then surveying a random sample within those regions is an effective method for large, geographically dispersed populations, known as cluster sampling. This approach helps ensure a diverse and representative sample of households across the city. Other options would introduce bias by focusing on specific locations or groups not representative of the entire city's households.
Question 3: What mode can you identify in the example below? <br> 11, 29, 21, 2, 28, 29, 18, 29, 6, 29, 29
- 28
- 21
- 15.5
- 29 (Correct answer)
Correct answer: 29
The mode of a data set is the value that appears most frequently. In the given set (11, 29, 21, 2, 28, 29, 18, 29, 6, 29, 29), the number 29 appears 5 times. Since no other number appears as often, 29 is the mode.
Question 4: What does the following sample mean look like? <br> 6, 4, 28, 21, 28, 28, 26, 28, 14, 9, 28
- 20 (Correct answer)
- 16
- 28
- 26
Correct answer: 20
The mean (average) is calculated by summing all the values in the data set and then dividing by the total number of values. For the given data (6, 4, 28, 21, 28, 28, 26, 28, 14, 9, 28), the sum is 220. Since there are 11 values, the mean is 220 divided by 11, which equals 20.
Question 5: For ten days, the number of patients Dr. Smith's dental practice saw each day was noted. Find the sample's mean, median, and mode using the provided data. <br> 3, 26, 8, 22, 30, 30, 6, 15, 21, 28
- 18.9, 30, 21.5
- 16.5, 30, 21.5
- 18.9, 21.5, 30 (Correct answer)
- 30, 21.5, 18.9
Correct answer: 18.9, 21.5, 30
First, order the data: 3, 6, 8, 15, 21, 22, 26, 28, 30, 30. The mean is the sum (189) divided by the count (10), which is 18.9. The median, for an even number of data points, is the average of the two middle values (21 and 22), so (21+22)/2 = 21.5. The mode is the value that appears most frequently, which is 30.
Question 6: In a math class, 50 percent of the pupils achieved an 80 on an accomplishment exam. With a few exceptions, the majority of the remaining pupils achieved scores of 72 or higher. Which of the following claims regarding the distribution of the scores is accurate?
- The mean is less than the median (Correct answer)
- The median is greater than the mode
- The mean and the median are the same
- The mean is greater than the mode
Correct answer: The mean is less than the median
If 50% of students scored exactly 80, the median score would be 80. The statement that the 'majority of the remaining pupils achieved scores of 72 or higher' implies there are some scores below 72. These lower scores would pull the mean down, making it less than the median of 80. This indicates a left-skewed distribution.
Question 7: A boy and a girl will be chosen to go to a conference from a group of five lads and two girls. How many different pairs are there to pick from?
- 15
- 10 (Correct answer)
- 20
- 5
Correct answer: 10
This is a combination problem where we need to choose one boy from five and one girl from two. The number of ways to choose 1 boy from 5 is 5 (C(5,1)). The number of ways to choose 1 girl from 2 is 2 (C(2,1)). To find the total number of different pairs, multiply these possibilities: 5 * 2 = 10.
Free CLAST Statistics and Probability Questions and Answers
A college president is curious about the most well-liked courses among students.
The president makes the decision to poll a representative sample of students.
Which method would be best for gathering a representative sample of college students from a statistically neutral perspective?