Q: A researcher collects the heights (in cm) of 100 students and organizes them into a frequency table with class intervals. What is the correct formula for the class width?

$$\text{class width} = \text{lower class limit of next class} - \text{lower class limit of current class}$$

Q: A class of 30 students took a test. The scores were grouped into intervals, and the frequency table was constructed. Which formula should be used to calculate the sample mean from this frequency table?

$$\bar{x} = \frac{\sum f \cdot \text{class midpoint}}{\sum f}$$

Q: A data set has the following five-number summary: minimum = 10, Q1 = 20, median = 30, Q3 = 40, maximum = 100. According to the outlier rule, is the value 100 an outlier?

Yes, because it is greater than $$Q_3 + 1.5$$ \times IQR$$

Question 1

A pharmaceutical company wants to test the effectiveness of a new drug. They randomly assign patients to either receive the drug or a placebo and follow them over time to observe outcomes. Which type of study is this?

Accepted Answer

Experimental study

Question 2

Which of the following best describes a variable that can only take on values such as 1, 2, 3, and so on, with no intermediate values possible?

Accepted Answer

Discrete variable

Question 3

A researcher collects the heights (in cm) of 100 students and organizes them into a frequency table with class intervals. What is the correct formula for the class width?

Accepted Answer

$$	ext{class width} = 	ext{lower class limit of next class} - 	ext{lower class limit of current class}$$

Question 4

Which of the following statements about the mean and median in a positively skewed distribution is correct?

Accepted Answer

Mean \u003e Median

Question 5

Given the following data set: 2, 4, 7, 10, 12, what is the sample mean?

Accepted Answer

$$7 ($$since \frac{2+4+7+10+12}{5} = 7)$

Question 6

A class of 30 students took a test. The scores were grouped into intervals, and the frequency table was constructed. Which formula should be used to calculate the sample mean from this frequency table?

Accepted Answer

$$\bar{x} = \frac{\sum f \cdot 	ext{class midpoint}}{\sum f}$$

Question 7

Which of the following is NOT a resistant measure of central tendency or spread?

Accepted Answer

Mean

Question 8

A data set has a mean of $$50$$ and a standard deviation of $$5. $$What is the z-score for a value of $$60$$?

Accepted Answer

$$z = 2$$

Question 9

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

Accepted Answer

$$	ext{IQR} = Q_3$ - Q_1$

Question 10

A boxplot of exam scores shows the median closer to the lower quartile (Q1) than the upper quartile (Q3), and the right whisker is longer than the left. What can you infer about the distribution?

Accepted Answer

The distribution is positively skewed

Question 11

If a data set has two modes, it is described as:

Accepted Answer

Bimodal

Question 12

Which of the following is the correct formula for the sample variance $$s^2$$?

Accepted Answer

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

Question 13

A hospital administrator wants to compare the average length of stay for patients in two different wards. Which type of data is being analyzed?

Accepted Answer

Quantitative (numerical)

Question 14

Which of the following best describes a systematic sample?

Accepted Answer

Every $$kth $$member of the population is selected after a random start

Question 15

A data set has the following five-number summary: minimum = 10, Q1 = 20, median = 30, Q3 = 40, maximum = 100. According to the outlier rule, is the value 100 an outlier?

Accepted Answer

Yes, because it is greater than $$Q_3 + 1.5$$ 	imes IQR$$

Question 16

Which of the following is true about the standard deviation?

Accepted Answer

It is measured in the same units as the original data

Question 17

A researcher wants to summarize the distribution of ages in a population. Which graphical method would be most appropriate?

Accepted Answer

Histogram

Question 18

If a value has a z-score of $$-2.5$$, what does this indicate?

Accepted Answer

The value is significantly low

Question 19

Which of the following best describes a boxplot?

Accepted Answer

It displays the five-number summary and potential outliers

Question 20

A data set has a mean of $$20$$ and a median of $$25. $$What can you infer about the skewness of the data?

Accepted Answer

The data is negatively skewed

Core Statistical Concepts and Data Summarization

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