Measures of Central Tendency Quiz

A numerical value that represents the central or typical value of a dataset. It summarizes the entire dataset with a single value, providing a sense of the overall trend.

A good average should be representative of the dataset, unaffected by extreme values, easy to calculate, and stable across different samples.

The most common type of average, calculated by summing all values in a dataset and dividing by the total number of values.

The average of a dataset, calculated by multiplying all values together and taking the nth root, where n is the number of values.

The average calculated by taking the reciprocal of the average of the reciprocals of all values in a dataset.

The middle value in a sorted dataset. It is the value that separates the lower half of the dataset from the upper half.

The value that appears most frequently in a dataset. It represents the most common value in the distribution.

The relationship between the mean, median, and mode describes the shape of the distribution. In a symmetrical distribution, all three measures tend to be equal. In a skewed distribution, the measures will differ.

The average of two or more distributions.

The symbol sigma (S) is used to denote the sum of a series of values.

The upper and lower limits of the summation index indicate the range of values to be included in the sum.

The average of a grouped frequency distribution is calculated by assuming all values in a class interval are concentrated around the midpoint of the interval.

The mean is sensitive to extreme values (outliers) in a dataset. They can significantly influence its value.

The mean is based on all values in a distribution, making it a comprehensive measure.

The mean can be used in further calculations and statistical analysis.

The mean is a stable measure, meaning it is relatively consistent across different samples from the same population.

The geometric mean (G.M.) is calculated by multiplying all values in a dataset and then taking the nth root, where n is the number of values.

The geometric mean is less affected by extreme values compared to the arithmetic mean.

The geometric mean is widely used in averaging ratios, percentages, and rates, especially when dealing with growth rates or compound interest.

The harmonic mean (H.M.) is the reciprocal of the average of the reciprocals of all values in a dataset.

The harmonic mean is particularly useful when dealing with averages of rates or speeds, especially when equal distances are covered at different rates.

The harmonic mean cannot be calculated if any value in the dataset is zero.

For any set of positive numbers, the arithmetic mean (A.M.) will always be greater than or equal to the geometric mean (G.M.), which will always be greater than or equal to the harmonic mean (H.M.).

The median is the middle value in a dataset when it's arranged in ascending or descending order.

If a dataset has an odd number of values, the median is the middle value. If it has an even number of values, the median is the average of the two middle values.

The median is less affected by extreme values than the arithmetic mean.

The median class is the class interval in a grouped frequency distribution that contains the median value.

For a grouped frequency distribution, the median is calculated by first determining the median class and then using the formula for a grouped frequency distribution.

The mode is the most frequently occurring value in a dataset.

The mode is useful for describing the most common value in a dataset, especially for categorical data.

In a symmetrical distribution, the mean, median, and mode tend to be equal. In a skewed distribution, they will differ.

The middle value in a sorted dataset. It divides the dataset into two equal halves - the lower half and the upper half.

The formula to calculate the median of a grouped frequency distribution is: Median = L + ((N/2 - fc)/f) * I where: L = Lower class limit of the median class, f = Frequency of the median class, fc = Cumulative frequency of the class preceding the median class, N = Total frequency, I = Class interval length

The formula to calculate the mode of a grouped frequency distribution is: Mode = L + ((f1 - f0)/(2f1 - f0 - f2)) * I where: L = Lower class limit of the modal class, f1 = Frequency of the modal class, f0 = Frequency of the class preceding the modal class, f2 = Frequency of the class succeeding the modal class, I = Class interval length.

A distribution with more than one mode. It has multiple peaks in its frequency graph.

A distribution with more than two modes. It has multiple high points in its frequency graph.

The median is a good measure of central tendency when dealing with datasets that have extreme values (outliers). It's less affected by these outliers compared to the mean.

The mode is useful for understanding the most popular or common value in a dataset. It helps businesses and industries understand trends and customer preferences.

The relationship between the mean, median, and mode in a distribution is often approximated by the formula: Mean - Mode = 3 (Mean - Median).

A type of central tendency that divides a dataset into four equal parts. There are three quartiles:

Values that divide a sorted dataset into ten equal parts. They allow for a more detailed analysis of the dataset than quartiles.

Values that divide a sorted dataset into one hundred equal parts. They are used for even finer granularity in analyzing the dataset.