Skip to main content
Back

Ch 3 - Statistics for Business: Measures of Central Tendency, Variation, and Relative Position

Control buttons has been changed to "navigation" mode.
1/20

Terms in this set (20)

  • What are the three main measures of central tendency?

    The three main measures of central tendency are mean, median, and mode.

  • How is the mean calculated?

    The mean is the arithmetic average, calculated by summing all values and dividing by the number of observations: \(\bar{x} = \frac{\sum x_i}{n}\).

  • What is a weighted mean and when is it used?

    The weighted mean assigns different weights to values, useful when some data points contribute more than others: \(\bar{x}_w = \frac{\sum w_i x_i}{\sum w_i}\).

  • How do you find the median in an ordered dataset?

    If the number of observations n is odd, the median is the value at position \(\frac{n+1}{2}\). If n is even, it is the average of values at positions \(\frac{n}{2}\) and \(\frac{n}{2}+1\).

  • What is the mode of a dataset?

    The mode is the value that appears most frequently. A dataset can have no mode, one mode (unimodal), or multiple modes (bimodal, multimodal).

  • What are the advantages and disadvantages of the mean?

    Advantages: Easy to calculate and widely used. Disadvantages: Affected by outliers. Applicable to interval and ratio data.

  • What are the advantages and disadvantages of the median?

    Advantages: Not affected by outliers. Disadvantages: Requires sorting data. Applicable to ordinal, interval, and ratio data.

  • What are the advantages and disadvantages of the mode?

    Advantages: Can be used with categorical data. Disadvantages: May not exist or may be multiple. Applicable to nominal, ordinal, interval, and ratio data.

  • Define the range as a measure of variation.

    The range is the difference between the highest and lowest values: \(R = \text{Highest value} - \text{Lowest value}\).

  • What is variance and how is it calculated for a sample?

    Variance is the average squared deviation from the mean. For a sample: \(s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1}\).

  • What is standard deviation and how is it related to variance?

    Standard deviation is the square root of the variance, expressed in the same units as the data: \(s = \sqrt{s^2}\).

  • What is the coefficient of variation (CV) and why is it useful?

    CV is the standard deviation as a percentage of the mean: \(CV = \frac{s}{\bar{x}} \times 100\%\). It allows comparison of variability between datasets with different units or means.

  • How do the mean and median relate in symmetric and skewed distributions?

    In symmetric distributions, mean = median. In left-skewed, mean < median. In right-skewed, mean > median.

  • What does a z-score represent and how is it calculated for a population?

    A z-score indicates how many standard deviations a value is from the mean. For a population: \(z = \frac{x - \mu}{\sigma}\).

  • State the Empirical Rule for normal distributions.

    Approximately 68% of data fall within ±1 standard deviation, 95% within ±2, and 99.7% within ±3 standard deviations of the mean.

  • What does Chebyshev’s Theorem state?

    For any distribution, at least \(1 - \frac{1}{k^2}\) of values fall within \(k\) standard deviations of the mean, for \(k > 1\).

  • What are percentiles and quartiles?

    Percentiles divide data into 100 equal parts; quartiles divide data into four equal parts: Q1 = 25th percentile, Q2 = 50th percentile (median), Q3 = 75th percentile.

  • How is the index for the pth percentile calculated?

    The index is \(i = \frac{p}{100} \times n\), where n is the number of data points.

  • What does a box-and-whisker plot display?

    A boxplot displays the five-number summary: minimum, Q1, median (Q2), Q3, and maximum. Outliers lie beyond \(Q1 - 1.5 \times IQR\) or \(Q3 + 1.5 \times IQR\).

  • How can Excel be used in descriptive statistics?

    Excel provides tools to calculate mean, median, mode, standard deviation, variance, percentiles, and to create boxplots and histograms using the Data Analysis Toolpak.