# FREE CLAST Statistics and Probability Questions and Answers

#### 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?

To select a statistically unbiased sample for estimating the average number of school-age children per house in the city, the most appropriate procedure would be to randomly select geographic regions of the city and then survey a random sample of people within those regions.

#### What does the following sample mean look like?

6, 4, 28, 21, 28, 28, 26, 28, 14, 9, 28

To find the mean (average) of a sample, you need to sum up all the values in the sample and then divide the sum by the number of values.

In the given sample, the sum of the values is:

6 + 4 + 28 + 21 + 28 + 28 + 26 + 28 + 14 + 9 + 28 = 220

There are 11 values in the sample, so to find the mean, divide the sum by the number of values:

220 / 11 = 20

Therefore, the mean of the sample is 20.

#### What mode can you identify in the example below?

11, 29, 21, 2, 28, 29, 18, 29, 6, 29, 29

In the given sample, the mode is the value that appears most frequently. In this case, the number 29 appears 4 times, which is more frequently than any other number in the sample. Therefore, the mode of the sample is 29.

#### 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?

To determine the number of different pairs that can be chosen from a group of five boys and two girls, we need to use the concept of combinations.

Since we are selecting one boy and one girl, we can choose one person from the group of five boys (5 options) and one person from the group of two girls (2 options).

To calculate the total number of different pairs, we multiply the number of options for each group:

Number of different pairs = Number of options for boys * Number of options for girls = 5 * 2 = 10

Therefore, there are 10 different pairs that can be chosen from the group of five boys and two girls to attend the conference.

#### 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?

To obtain a statistically unbiased sample of the college's students, the most appropriate procedure would be to survey a random sample of students from a list of the entire student body.

#### 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.

3, 26, 8, 22, 30, 30, 6, 15, 21, 28

#### 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 statement "The mean is less than the median" is true about the distribution of the scores.

In this scenario, half of the students scored 80, which indicates that the majority of the scores are clustered around 80. Most of the remaining students scored 72, suggesting a slight skew towards the lower end. Additionally, a few students scored 24, which are significantly lower than the rest of the scores.