Skip to main content
Indietro

Introductory Statistics: Measures of Center, Variation, and Relative Standing

I pulsanti di controllo sono stati cambiati in modalità "navigazione".
1/25

Termini in questo insieme (25)

  • What is a measure of center in statistics?

    A measure of center is a value that represents the middle or center of a data set in some way.

  • Define the mean and its symbols.

    The mean is the sum of all data values divided by the number of values. Sample mean is \(\bar{x}\), population mean is \(\mu\).

  • What is the median of a data set?

    The median is the middle value of ordered data. If even number of values, it is the mean of the two middle values.

  • Explain the mode and its applicability.

    The mode is the most frequently occurring data value. It can be used for both quantitative and categorical data.

  • What is the midrange of a data set?

    The midrange is the mean of the maximum and minimum values: (max + min) / 2.

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

    A weighted mean accounts for different weights assigned to data values, calculated as sum of (weight × value) divided by sum of weights.

  • Which measures of center are resistant to outliers?

    The median is resistant to outliers; the mean and midrange are not resistant.

  • Define a measure of variation in statistics.

    A measure of variation quantifies the spread or dispersion of data values.

  • What is the range of a data set?

    The range is the difference between the maximum and minimum data values.

  • What does the standard deviation measure?

    Standard deviation measures how far data values typically vary from the mean.

  • How is variance related to standard deviation?

    Variance is the square of the standard deviation, representing average squared deviation from the mean.

  • What is the range rule of thumb for estimating standard deviation?

    Estimate standard deviation as approximately one-fourth of the range: s ≈ (max − min) / 4.

  • When is a data value considered significantly high or low?

    Values are significantly high if > mean + 2 standard deviations, and significantly low if < mean − 2 standard deviations.

  • State the Empirical Rule for normal distributions.

    For bell-shaped data: ~68% within 1 SD, ~95% within 2 SDs, ~99.7% within 3 SDs of the mean.

  • What is a z-score and how is it interpreted?

    A z-score indicates how many standard deviations a data value is from the mean; positive means above, negative means below.

  • How do you calculate the z-score for a sample data value?

    Sample z-score: \(z=\frac{x-\bar{x}}{s}\), where \(x\) is the data value.

  • What are percentiles in a data set?

    Percentiles divide ordered data into 100 groups; the kth percentile is the value below which approximately k% of data fall.

  • How is the kth percentile data value found?

    Arrange data, compute locator L = kn/100; if L integer, average Lth and (L+1)th values; if not, round up and take Lth value.

  • What are quartiles and the 5-number summary?

    Quartiles divide data into 4 parts: Q1 (25th percentile), Q2 (median), Q3 (75th percentile). The 5-number summary includes min, Q1, median, Q3, max.

  • What is a boxplot and what does it show?

    A boxplot visualizes the 5-number summary with a box from Q1 to Q3, a line at the median, and whiskers to min and max values.

  • Define the interquartile range (IQR).

    The IQR is the range of the middle 50% of data: IQR = Q3 − Q1.

  • How are outliers identified using the IQR?

    Outliers are values < Q1 − 1.5·IQR or > Q3 + 1.5·IQR.

  • How can boxplots indicate skewness?

    Skewness is shown by asymmetry in boxplot whiskers or box width; longer whisker or wider box on one side indicates skew.

  • What is the difference between biased and unbiased estimators?

    Unbiased estimators tend to center around the true parameter value; biased estimators do not.

  • Give examples of unbiased and biased estimators.

    Unbiased: sample mean \(\bar{x}\), sample variance \(s^2\). Biased: sample median, sample range, sample standard deviation \(s\).