Calculating the Mean: Understanding Incorrect Arithmetic Mean

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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?

0 Signup and view all the answers

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

Birr 277.33 Signup and view all the answers

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

54 Signup and view all the answers

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

The dataset is unimodal. Signup and view all the answers

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

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

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

Because it is not affected by extreme values. Signup and view all the answers

What is the purpose of the median in a dataset?

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

What is the modal class in a grouped dataset?

The class with the maximum frequency. Signup and view all the answers

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

Because it is affected by extreme values. Signup and view all the answers

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

Harmonic mean Signup and view all the answers

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

AM ≥ GM ≥ HM Signup and view all the answers

What is the limitation of calculating the harmonic mean?

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

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

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

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

Multi-modal Signup and view all the answers

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

It is the value that occurs most frequently in the dataset Signup and view all the answers