Q: A researcher wants to identify outliers in a data set using the IQR method. Which formula should they use to determine the lower and upper bounds?

Lower bound: $$Q_1 - 1.5$$ \times IQR$$, Upper bound: Q_3$ + 1.5 \times IQR$$

Question 1

A researcher collects the following data set of exam scores: 55, 60, 65, 70, 95. Which measure of central tendency is most affected by the outlier in this data set?

Accepted Answer

Mean

Question 2

Given the following frequency distribution of test scores:

Score: 70, 80, 90, 100
Frequency: 2, 3, 4, 1

What is the mean score?

Use the formula: $$	ext{Mean} = \frac{\sum f_i x_i}{\sum f_i}$$

Accepted Answer

Mean = 85.5

Question 3

A sample of systolic blood pressure readings has a mean of 120 mmHg and a standard deviation of 15 mmHg. What is the coefficient of variation (CV)?

Use the formula: $$CV = \frac{	ext{Standard Deviation}}{	ext{Mean}} 	imes 100\%$$

Accepted Answer

CV = 12.5\%

Question 4

Which of the following statements about the Empirical Rule is correct for a normal distribution?

Accepted Answer

Approximately 95\% of data falls within two standard deviations of the mean.

Question 5

A student scored 82 on a test where the mean was 75 and the standard deviation was 7. What is the student's z-score?

Use the formula: $$z = \frac{X - \mu}{\sigma}$$

Accepted Answer

z = 1

Question 6

Which of the following best describes an outlier in a data set?

Accepted Answer

A value that is far removed from the rest of the data

Question 7

A box and whisker plot is used to display which of the following features of a data set?

Accepted Answer

Quartiles, median, and outliers

Question 8

If the interquartile range (IQR) of a data set is 20, and the first quartile ($$Q_1) is 30$$, what is the third quartile ($$Q_3$$)?

Use the formula: $$IQR = Q_3$ - Q_1$

Accepted Answer

$$Q_3 = 50$

Question 9

Chebychev’s Theorem states that for any data set (regardless of distribution), at least what percentage of values lie within $$k$$ standard deviations of the mean, where $$k \u003e 1$$?

Use the formula: $$1 - \frac{1}{k^2$}$$

Accepted Answer

At least $$1 - \frac{1}{k^2$} of $$the data

Question 10

A data set has a mean of 50 and a variance of 25. What is the standard deviation?

Use the formula: $$\sigma = \sqrt{	ext{Variance}}$$

Accepted Answer

$$\sigma = 5$$

Question 11

Which scenario best illustrates the use of a weighted mean?

Accepted Answer

Calculating a student's GPA where courses have different credit hours

Question 12

A sample of 5 measurements has the following values: 10, 12, 14, 16, 18. What is the sample mean?

Use the formula: $$\bar{x} = \frac{\sum x_i}{n}$$

Accepted Answer

Sample mean = 14

Question 13

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

Accepted Answer

Range

Question 14

A distribution is symmetric and bell-shaped. Which measure of central tendency will be equal?

Accepted Answer

Mean, median, and mode

Question 15

A sample of 10 students has a mean height of 170 cm and a sample standard deviation of 8 cm. What is the variance?

Use the formula: $$s^2$$ = (	ext{Sample Standard Deviation}$$)^2$$

Accepted Answer

Variance = 64

Question 16

Which of the following best describes the interquartile range (IQR)?

Accepted Answer

The difference between the third and first quartiles

Question 17

A data set has the following values: 2, 4, 4, 4, 5, 6, 8. What is the mode?

Accepted Answer

Mode = 4

Question 18

If a data set has a range of 40 and the minimum value is 10, what is the maximum value?

Accepted Answer

Maximum = 50

Question 19

A researcher wants to identify outliers in a data set using the IQR method. Which formula should they use to determine the lower and upper bounds?

Accepted Answer

Lower bound: $$Q_1 - 1.5$$ 	imes IQR$$, Upper bound: Q_3$ + 1.5 	imes IQR$$

Question 20

Which of the following is true about the shape of a distribution that is positively skewed?

Accepted Answer

The mean is greater than the median

Statistical Measures: Central Tendency and Dispersion

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