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Introductory Statistics Key Concepts

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Terms in this set (20)

  • What is the difference between a sample and a population?

    A population includes all members of a group being studied, while a sample is a subset of the population used to make inferences.

  • Define quantitative and qualitative data.

    Quantitative data are numerical and measurable, while qualitative data are descriptive and categorical.

  • What is a blind study?

    A blind study is one where participants do not know which treatment they receive to prevent bias.

  • What is a double blind study?

    A double blind study is one where neither participants nor experimenters know who receives the treatment, reducing bias further.

  • What are nominal, interval, and ratio scales?

    Nominal: categories without order; Interval: ordered with equal intervals but no true zero; Ratio: ordered with equal intervals and a true zero.

  • How do you identify unusual or very unusual data points on charts?

    Data points far from the mean or outside typical ranges, often beyond 2 or 3 standard deviations, are considered unusual or very unusual.

  • What is frequency in statistics?

    Frequency is the number of times a data value or category occurs in a dataset.

  • What is the formula for the mean?

    The mean is the sum of all data values divided by the number of values: \(\bar{x} = \frac{\sum x_i}{n}\).

  • What is standard deviation?

    Standard deviation measures the average distance of data points from the mean, indicating data spread.

  • What is the formula for population standard deviation?

    Population standard deviation: \(\sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}}\).

  • What is the formula for sample standard deviation?

    Sample standard deviation: \(s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}\).

  • What does the notation X minus MSSX represent?

    X minus MSSX refers to the deviation of a data point from the mean, i.e., \(x_i - \bar{x}\).

  • What is the empirical rule in statistics?

    The empirical rule states that for normal distributions, about 68% of data lie within 1 standard deviation, 95% within 2, and 99.7% within 3.

  • How do you arrange data to find the range?

    Arrange data in order and subtract the smallest value from the largest to find the range.

  • What is the interquartile range (IQR)?

    The IQR is the difference between the third quartile (Q3) and first quartile (Q1), measuring the middle 50% spread.

  • What is variance in statistics?

    Variance is the average of squared deviations from the mean, representing data spread.

  • What is Chebyshev's theorem?

    Chebyshev's theorem states that for any distribution, at least 1 - 1/k² of data lies within k standard deviations of the mean, for k > 1.

  • How is standard deviation related to variance?

    Standard deviation is the square root of the variance.

  • What is the difference between population variance and sample variance?

    Population variance divides by N; sample variance divides by n-1 to correct bias.

  • What is the purpose of frequency charts and graphs?

    They visually display data distribution and frequency of values or categories.