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Chapter 3: Measures of Center, Variation, and Data Distribution

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Termini in questo insieme (20)

  • What is the mean of a data set?

    The mean is the arithmetic average, found by summing all data values and dividing by the number of values.

  • How is the median defined in a data set?

    The median is the middle value when data are ordered from least to greatest. It divides the data into two equal halves.

  • What is the mode of a data set?

    The mode is the value that appears most frequently in the data set.

  • Define the midrange of a data set.

    The midrange is the average of the minimum and maximum values: \(\frac{\text{min} + \text{max}}{2}\).

  • Which measures of center are resistant to outliers?

    The median and mode are resistant to outliers, while the mean and midrange are sensitive to extreme values.

  • What is the range of a data set?

    The range is the difference between the maximum and minimum values: \(\text{max} - \text{min}\).

  • How is variance calculated?

    Variance is the average of the squared differences from the mean.

  • What does the standard deviation represent?

    Standard deviation is the square root of the variance and measures the average distance of data values from the mean.

  • Which measures of variation are sensitive to outliers?

    Range, variance, and standard deviation are sensitive to outliers because they depend on extreme values.

  • What does it mean for a data value to be significantly high or low?

    A data value is significantly high or low if it is far from the mean, often identified using z-scores or being outside typical ranges.

  • State the Empirical Rule for data distribution.

    The Empirical Rule states that for a normal distribution, about 68% of data lie within 1 standard deviation, 95% within 2, and 99.7% within 3 standard deviations of the mean.

  • What is a z-score and what does it indicate?

    A z-score measures how many standard deviations a data value is from the mean, indicating its relative position.

  • How do you interpret a z-score of +2?

    A z-score of +2 means the data value is 2 standard deviations above the mean, which is relatively high.

  • What is a percentile in a data set?

    A percentile indicates the percentage of data values below a given value in the ordered data set.

  • What does the 25th percentile represent?

    The 25th percentile (first quartile) is the value below which 25% of the data fall.

  • What is the 5-number summary of a data set?

    The 5-number summary includes the minimum, first quartile (Q1), median, third quartile (Q3), and maximum values.

  • How are quartiles related to percentiles?

    Quartiles divide data into four equal parts; Q1 is the 25th percentile, Q2 (median) is the 50th, and Q3 is the 75th percentile.

  • Why is the median preferred over the mean for skewed data?

    The median is preferred because it is resistant to outliers and skewed values, providing a better center measure for skewed data.

  • What does a z-score near 0 indicate about a data value?

    A z-score near 0 means the data value is close to the mean.

  • How can the 5-number summary help describe data distribution?

    The 5-number summary provides a quick overview of data spread, center, and potential outliers.