Measures of Central Tendency

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Questions and Answers

What is the primary purpose of measures of central tendency?

  • To describe the central value of a data set (correct)
  • To categorize data into groups
  • To identify extreme values in the data
  • To analyze the spread of data values

Which measure of central tendency is most affected by outliers?

  • Median
  • Mode
  • Mean (correct)
  • Range

In what situation is the median considered a better measure of central tendency than the mean?

  • When all values are the same
  • When data is normally distributed
  • When data shows a bimodal distribution
  • When there are extreme values in the data (correct)

What is a disadvantage of using the mode as a measure of central tendency?

<p>It does not consider all data points (D)</p> Signup and view all the answers

Which statement best describes the characteristics of the mode?

<p>It can have multiple values in bimodal or multimodal distributions (C)</p> Signup and view all the answers

For which type of data distribution is the arithmetic mean typically the best choice?

<p>Normal distribution (D)</p> Signup and view all the answers

Which of the following statements is true regarding the median?

<p>It is less influenced by extreme values than the mean (A)</p> Signup and view all the answers

What should influence the choice of the appropriate measure of central tendency?

<p>The nature of the data and analysis goals (A)</p> Signup and view all the answers

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Study Notes

mjera centralne tendencije

  • Definicija: Mjera centralne tendencije opisuje centralnu ili "srednju" vrijednost skupa podataka.

  • Tipovi mjera:

    1. Aritmetička sredina:
      • Zbrajanje svih vrijednosti i dijeljenje s brojem vrijednosti.
      • Osjetljiva na ekstremne vrijednosti (outliers).
    2. Medijan:
      • Srednja vrijednost skupa kada su podaci poredani.
      • Manje osjetljiv na ekstremne vrijednosti.
    3. Mod:
      • Najčešće se pojavljujuća vrijednost u skupu podataka.
      • Može postojati više modova (bimodalni, multimodalni).
  • Primjena:

    • Korištenje u statistici i analizi podataka.
    • Pomoć pri opisu i poređenju podataka.
    • Korisno u donošenju odluka temeljeno na analizama.
  • Prednosti i nedostaci:

    • Aritmetička sredina:
        • Jednostavna za izračunavanje i interpretaciju.
        • Može biti pristrana zbog ekstremnih vrijednosti.
    • Medijan:
        • Otporniji na utjecaj ekstremnih vrijednosti.
        • Ne uzima u obzir sve podatke.
    • Mod:
        • Prikazuje najčešće pojavljivanje.
        • Može biti nepouzdan u malim skupovima.
  • Izbor prave mjere:

    • Odabir mjere centralne tendencije ovisi o prirodi podataka i ciljevima analize.
    • Za normalno distribuirane podatke, aritmetička sredina je često najbolji izbor.
    • Za asimetrične distribucije, medijan može biti bolji odabir.

Measures of Central Tendency

  • Definition: Measures of central tendency describe the central or "average" value of a dataset.
  • Types of Measures:
    • Arithmetic Mean: Sum of all values divided by the number of values. Sensitive to outliers.
    • Median: Middle value of a dataset when ordered. Less sensitive to outliers.
    • Mode: Most frequently occurring value in a dataset. Can have multiple modes (bimodal, multimodal).
  • Applications:
    • Used in statistics and data analysis.
    • Help to describe and compare data.
    • Useful in making decisions based on analysis.
  • Advantages and Disadvantages:
    • Arithmetic Mean:
      • + Simple to calculate and interpret.
      • - Can be biased due to extreme values.
    • Median:
      • + Resistant to the influence of extreme values.
      • - Doesn't consider all data.
    • Mode:
      • + Shows the most frequent occurrence.
      • - Can be unreliable in small datasets.
  • Choosing the Right Measure:
    • The choice of central tendency measure depends on the nature of the data and the goals of the analysis.
    • For normally distributed data, the arithmetic mean is often the best choice.
    • For asymmetric distributions, the median might be a better selection.

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