Here are the answers and explanations for each question:

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

   • Answer: C) Standard deviation
     • Explanation: Measures of central tendency describe the center of a data set, and include the mean, median, and mode. Standard deviation is a measure of spread, not central tendency.

2. A data set has a mean of 50 and a median of 60. Which of the following best describes its distribution?

   • Answer: B) Positively skewed
     • Explanation: In a positively skewed distribution, the mean is typically less than the median because extreme high values pull the mean upward.

3. The interquartile range (IQR) measures:

   • Answer: C) The range of the middle 50% of the data
     • Explanation: The IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1), capturing the spread of the middle 50% of the data.

4. If two events, A and B, are independent, then:

   • Answer: B) P(A ∩ B) = P(A)*P(B)
     • Explanation: For independent events, the probability of both occurring is the product of their individual probabilities.

5. For a normal distribution, approximately what percentage of data falls within 1.5 standard deviations of the mean?

   • Answer: B) 87%
     • Explanation: Approximately 87% of the data in a normal distribution falls within 1.5 standard deviations from the mean, derived from empirical rules or cumulative probability tables.

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Do you want a detailed explanation or visualization of any of these? Here are 5 related questions for further exploration:

1. What are some other measures of spread besides standard deviation and IQR?
2. How do you determine whether a data set is skewed positively or negatively?
3. Can you calculate IQR given a small data set?
4. What is the difference between dependent and independent events in probability?
5. How does the empirical rule help estimate probabilities in a normal distribution?

Tip: Always check the shape of a distribution visually (e.g., histogram or box plot