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Introductory Statistics: Key Concepts and Formulas

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Termini in questo insieme (29)

  • What is a frequency distribution?
    A table showing classes or intervals of data with lower and upper limits, class width, and frequencies.
  • How do you calculate the class width in a frequency distribution?
    Class width = (Range) ÷ (Number of classes), rounded up to a convenient number.
  • What is the range of a data set?
    The difference between the maximum and minimum data entries.
  • How is the midpoint of a class interval calculated?
    Midpoint = (Lower class limit + Upper class limit) ÷ 2.
  • Define relative frequency.
    Relative frequency = Class frequency ÷ Sample size (f/n), representing the portion of data in a class.
  • What is cumulative frequency?
    The sum of the frequency for a class and all previous classes.
  • Describe a frequency histogram.
    A bar graph representing frequency distribution with quantitative horizontal scale and touching bars at class boundaries.
  • What is a frequency polygon?
    A line graph showing continuous change in frequencies using midpoints, starting and ending on the horizontal axis.
  • How is a pie chart constructed?
    A circle divided into sectors proportional to category frequencies; central angle = 360° × relative frequency.
  • What is a Pareto chart?
    A vertical bar graph with bars ordered from tallest to shortest, representing frequency or relative frequency.
  • Define a paired data set and its graphical representation.
    Two related data sets graphed as ordered pairs on a scatter plot to show relationships between two quantitative variables.
  • What is the mean of a data set?
    The sum of all data entries divided by the number of entries.
  • What is the median?
    The middle value of an ordered data set; if even number of entries, the mean of the two middle values.
  • Define mode in a data set.
    The data entry with the greatest frequency; no mode if no repeats; multiple modes if tied frequencies.
  • What is the formula for weighted mean?
    Weighted mean = \(\frac{\sum xw}{\sum w}\), where w is the weight of each entry x.
  • Describe a symmetric distribution.
    A distribution where mean, median, and mode are equal and the graph is roughly mirrored on both sides.
  • What characterizes a skewed left distribution?
    The tail elongates to the left; mean is less than the median.
  • How is range calculated?
    Range = Maximum data entry − Minimum data entry.
  • What is deviation in statistics?
    The difference between a data entry x and the mean: for population, x − μ; for sample, x − \(\bar{x}\).
  • What is the population variance formula?
    Population variance: \(\sigma^2 = \frac{\sum (x - \mu)^2}{N}\).
  • What is the sample variance formula?
    Sample variance: \(s^2 = \frac{\sum (x - \bar{x})^2}{n - 1}\).
  • State Chebyshev’s Theorem.
    At least \(1 - \frac{1}{k^2}\) of data lies within k standard deviations of the mean, for k > 1.
  • What is the coefficient of variation (CV)?
    CV expresses standard deviation as a percent of the mean: Population CV = \(\frac{\sigma}{\mu} \times 100\%\), Sample CV = \(\frac{s}{\bar{x}} \times 100\%\).
  • What are quartiles?
    Values dividing ordered data into four equal parts: Q1 (25%), Q2 (median, 50%), Q3 (75%).
  • How is the interquartile range (IQR) calculated?
    IQR = Q3 − Q1, measuring the range of the middle 50% of data.
  • How do you identify outliers using IQR?
    Outliers are data points less than Q1 − 1.5(IQR) or greater than Q3 + 1.5(IQR).
  • What is a box-and-whisker plot?
    A graph showing minimum, Q1, median (Q2), Q3, and maximum to highlight data distribution.
  • How is a percentile calculated for a data entry x?
    Percentile = (Number of data entries less than x ÷ Total number of entries) × 100, rounded to nearest whole number.
  • What is a z-score?
    The number of standard deviations a value x is from the mean: \(z = \frac{x - \mu}{\sigma}\).