Calculating the Mean: Understanding Incorrect Arithmetic Mean
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Questions and Answers

What is the formula to calculate the correct mean when there is an incorrect observation?

  • ∑Xcorrect = n∑f - misread observation(s) + correct observation(s)
  • ∑Xcorrect = n∑f + misread observation(s) - correct observation(s)
  • ∑Xcorrect = ∑Xincorrect + misread observation(s) - correct observation(s)
  • ∑Xcorrect = ∑Xincorrect - misread observation(s) + correct observation(s) (correct)

    • What happens to the arithmetic mean when every value of the variable X is increased by a constant (K)?

  • It increases by K (correct)
  • It remains the same
  • It decreases by K
  • It gets multiplied by K

    • What is the name of the average calculated from grouped data?

  • Geometric Mean
  • Mode
  • Median
  • Arithmetic Mean (correct)

    • What is the sum of the deviations of a set of values from their arithmetic mean?

    <p>0</p> Signup and view all the answers

    What is the correct mean wage in the example given in the text?

    <p>Birr 277.33</p> Signup and view all the answers

    What is the total number of observations in the given frequency distribution?

    <p>54</p> Signup and view all the answers

    What is the assumption about the dataset in calculating the mode for grouped data?

    <p>The dataset is unimodal.</p> Signup and view all the answers

    What is the formula to calculate the mode for grouped data?

    <p>Mode = L + (Δ1 / (Δ1+Δ2)) x W</p> Signup and view all the answers

    Why is the median considered a suitable average in a dataset with extreme values?

    <p>Because it is not affected by extreme values.</p> Signup and view all the answers

    What is the purpose of the median in a dataset?

    <p>To divide the ordered set of observations into two equal halves.</p> Signup and view all the answers

    What is the modal class in a grouped dataset?

    <p>The class with the maximum frequency.</p> Signup and view all the answers

    Why is the mean not suitable for a dataset with extreme values?

    <p>Because it is affected by extreme values.</p> Signup and view all the answers

    What is the most suitable average to use when analyzing phenomena involving rate and price?

    <p>Harmonic mean</p> Signup and view all the answers

    What is the relationship between the arithmetic mean, geometric mean, and harmonic mean for all positive observations?

    <p>AM ≥ GM ≥ HM</p> Signup and view all the answers

    What is the limitation of calculating the harmonic mean?

    <p>It cannot be calculated when at least one of the observations is zero</p> Signup and view all the answers

    What is the formula to calculate the harmonic mean if the arithmetic mean and geometric mean are known?

    <p>HM = (GM)^2 / AM</p> Signup and view all the answers

    What is the term used to describe a distribution with more than two modes?

    <p>Multi-modal</p> Signup and view all the answers

    What is the primary characteristic of the mode in a dataset?

    <p>It is the value that occurs most frequently in the dataset</p> Signup and view all the answers

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