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 (B)</p>
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What is the correct mean wage in the example given in the text?

<p>Birr 277.33 (C)</p>
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What is the total number of observations in the given frequency distribution?

<p>54 (A)</p>
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What is the assumption about the dataset in calculating the mode for grouped data?

<p>The dataset is unimodal. (A)</p>
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What is the formula to calculate the mode for grouped data?

<p>Mode = L + (Δ1 / (Δ1+Δ2)) x W (B)</p>
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Why is the median considered a suitable average in a dataset with extreme values?

<p>Because it is not affected by extreme values. (A)</p>
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What is the purpose of the median in a dataset?

<p>To divide the ordered set of observations into two equal halves. (C)</p>
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What is the modal class in a grouped dataset?

<p>The class with the maximum frequency. (D)</p>
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Why is the mean not suitable for a dataset with extreme values?

<p>Because it is affected by extreme values. (C)</p>
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What is the most suitable average to use when analyzing phenomena involving rate and price?

<p>Harmonic mean (D)</p>
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What is the relationship between the arithmetic mean, geometric mean, and harmonic mean for all positive observations?

<p>AM ≥ GM ≥ HM (D)</p>
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What is the limitation of calculating the harmonic mean?

<p>It cannot be calculated when at least one of the observations is zero (A)</p>
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What is the formula to calculate the harmonic mean if the arithmetic mean and geometric mean are known?

<p>HM = (GM)^2 / AM (A)</p>
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What is the term used to describe a distribution with more than two modes?

<p>Multi-modal (C)</p>
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What is the primary characteristic of the mode in a dataset?

<p>It is the value that occurs most frequently in the dataset (D)</p>
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