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Measures of Central Tendency: Mean

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Questions and Answers

Which measure of central tendency is used when the distribution contains extreme values?

Mean

Median (correct)

Mode

All of the above

What is the primary purpose of using the mean as a measure of central tendency?

To minimize the effect of extreme values

To find the most frequently occurring value

To divide the data into two equal parts

To include all the given values in the computation (correct)

When is the median the most appropriate measure of central tendency to use?

When the data is ordinal or ranked (correct)

When the greatest reliability of the measure is required

When the distribution contains extreme values

When higher statistical computations are needed

What is the formula for calculating the median of an even number of values?

The average of the two middle values (B) Signup and view all the answers

Which measure of central tendency is most affected by extreme values in a distribution?

Mean (A) Signup and view all the answers

Which measure of central tendency is used when the goal is to find the most frequently occurring value in a dataset?

Mode (C) Signup and view all the answers

Which of the following measures describes the spread of a data set around the central value?

Standard deviation (B) Signup and view all the answers

If the range of a data set is small, what can be inferred about the variation?

The data points are closely clustered around the mean. (B) Signup and view all the answers

Which measure of variation is most affected by outliers?

Variance (D) Signup and view all the answers

If the standard deviation of a data set is zero, what can be concluded?

All data points are equal to the mean. (C) Signup and view all the answers

Which measure of variation is most appropriate for comparing the spread of two data sets with different units?

Coefficient of variation (A) Signup and view all the answers

What is the relationship between the mean deviation and the standard deviation?

The mean deviation is always less than the standard deviation. (A) Signup and view all the answers

What is the most reliable and sensitive measure of central tendency?

Mean (C) Signup and view all the answers

What is the formula for calculating the simple mean?

$\bar{x} = \frac{\sum{x}}{n}$ (D) Signup and view all the answers

What is the difference between the simple mean and the weighted mean?

The simple mean is calculated by adding all the values and dividing by the number of values, while the weighted mean is calculated by multiplying each value by its weight and then dividing by the sum of the weights. (A) Signup and view all the answers

Which of the following is not a common measure of central tendency?

Standard deviation (D) Signup and view all the answers

If the scores of 15 students in a 25-item test are 15, 18, 17, 16, 19, 21, 18, 23, 24, 18, 16, 17, 20, 21, and 19, what is the mean score of the students?

18.80 (A) Signup and view all the answers