Central tendency refers to the tendency of a given set of observations to cluster around ___ and ___ values.

What is the primary purpose of computing measures of central tendency in data analysis?

To condense a large amount of data into a single representative value.

The Arithmetic Mean (AM) is calculated by ___ the sum of all observations and dividing it by the total number of observations.

Taking

List two advantages of using the Median as a measure of central tendency.

It is less affected by extreme values and is straightforward to compute.

True or False: The Mode is always guaranteed to exist in a dataset.

False. A mode may not exist if all values are unique.

What is the relationship between the Arithmetic Mean, Geometric Mean, and Harmonic Mean for any set of positive observations?

AM ≥ GM ≥ HM, with equality when all observations are equal.

Fill in the blank: To find Quartiles in a dataset, we divide the observations into ___ equal parts.

Four

In a frequency distribution, how is the combined Arithmetic Mean computed when two groups are involved?

By using the formula AM_combined = (n₁AM₁ + n₂AM₂) / (n₁ + n₂), where n is the number of observations.

What is the formula for the Geometric Mean (GM) for a set of n positive observations?

The first quartile (Q₁) represents the value below which ___ percent of the data falls.

25

True or False: The Mode can have multiple values in a dataset.

True. A dataset can be unimodal, bimodal, or multimodal.

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

It lacks mathematical properties and can be undefined.

Fill in the blanks: The ___ Mean is appropriate for calculating average rates, while the ___ Mean is best for data with rates and ratios.

Harmonic; Geometric