Question 1

Given the data set: 1, 3, 5, 7, 3, 3, 2, 7, 8, 2, 4, 9, 10, what is the range of the data?

Accepted Answer

$$10 - 1 = 9$$

Question 2

For the data set: 0, 6, -3, 5, -12, 4, 17, 3, -9, 10, -3, 2, 0, what is the median?

Accepted Answer

$$0$$

Question 3

Which of the following is the correct formula for the sample variance $$s^2 of a $$data set with $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$ and sample mean $$\bar{x}$$?

Accepted Answer

$$s^2$$ = \frac{\sum_{i=1}^n (x_i - \bar{x}$$)^2$$}{n-1}$$

Question 4

A data set has the following values: 1.1, 1.2, 1.2, 1.3, 1.2, 1.1, 2.2, 1.5, 1.6, 1.4, 1.7, 1.4, 1.9. What is the mode of this data set?

Accepted Answer

$$1.2$$

Question 5

Given the data set: 25, 25, 24, 24, 16, 16, 16, 23, 24, 25, 27, 28, 29, 31, 32, 34, 34, 12, 15, 17, 15, 15, what is the mean (rounded to two decimal places)?

Accepted Answer

$$23.82$$

Question 6

Which of the following statements is TRUE regarding the difference between sample standard deviation and population standard deviation?

Accepted Answer

Sample standard deviation divides by $$n-1$$, while population standard deviation divides by $$n.$$

Question 7

A researcher collects the following data: 0, 6, -3, 5, -12, 4, 17, 3, -9, 10, -3, 2, 0. What is the sample variance of the data? (Round to two decimal places)

Accepted Answer

$$60.92$$

Question 8

If a data set has a sample variance $$s^2 = 25$, what is the sample standard deviation s$?

Accepted Answer

$$5$$

Question 9

Which of the following best describes the effect of an outlier on the mean and median of a data set?

Accepted Answer

The mean is more affected by outliers than the median.

Question 10

A data set consists of the following values: 2, 4, 4, 4, 5, 5, 7, 9. What is the median?

Accepted Answer

$$4.5$$

Question 11

Given a population data set $$x_1$$, $$x_2$$, ..., x_N$$ with mean $$\mu$$, which formula correctly calculates the population variance $$\$$sigma^2$$?

Accepted Answer

$$\$$sigma^2$$ = \frac{\sum_{i=1}^N (x_i - \mu)^2$}{N}$$

Question 12

A hospital records the number of patients admitted each day for a week: 12, 15, 14, 13, 15, 16, 15. What is the mode?

Accepted Answer

$$15$$

Question 13

A data set has the following values: 1, 3, 5, 7, 3, 3, 2, 7, 8, 2, 4, 9, 10. What is the sample standard deviation? (Round to two decimal places)

Accepted Answer

$$2.68$$

Question 14

Which of the following is NOT a measure of central tendency?

Accepted Answer

Variance

Question 15

A chemist measures the concentration of a solution in 5 samples: 1.2, 1.3, 1.1, 1.4, 1.2. What is the population standard deviation? (Round to two decimal places)

Accepted Answer

$$0.11$$

Question 16

A data set has a mean of $$10$$ and a standard deviation of $$2. If $$every value in the data set is increased by $$5$$, what will be the new mean and standard deviation?

Accepted Answer

Mean: $$15$$, Standard deviation: $$2$$

Question 17

A data set has the following values: 0, 6, -3, 5, -12, 4, 17, 3, -9, 10, -3, 2, 0. What is the population variance? (Round to two decimal places)

Accepted Answer

$$56.23$$

Question 18

Which of the following best describes the relationship between variance and standard deviation?

Accepted Answer

Standard deviation is the square root of variance.

Question 19

A teacher records the following test scores: 80, 85, 90, 95, 100. What is the range?

Accepted Answer

$$100 - 80 = 20$$

Question 20

A data set has the following values: 1.1, 1.2, 1.2, 1.3, 1.2, 1.1, 2.2, 1.5, 1.6, 1.4, 1.7, 1.4, 1.9. What is the sample mean? (Round to two decimal places)

Accepted Answer

$$1.46$$

Step-by-Step Guidance for Descriptive Statistics: Range, Median, Mode, Mean, Variance, and Standard Deviation

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