Calculating Median and Mode of a Data Set

Median Median refers to the midpoint or the middle value of a data set after sorting the values in ascending or descending order. Our data set sorted in ascending order is presented below: 1.2, 1.5, 1.7, 2.3, 2.5, 2.9, 3, 3.8, 4.2, 4.3, 5.4, 5.5, 5.6, 5.9, 6.2, 6.7,...

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Calculating Harmonic Mean

Harmonic mean is calculated by dividing the number of observations (n) by the sum of reciprocals of all observations. Harmonic mean has some applications in finance. One application is to calculate the average purchase cost of shares purchased over time. Let’s say...

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Calculating Geometric Mean

One problem with arithmetic mean is that it assumes the returns on the investment made at the beginning of each period. So, for each period the beginning investment amount is assumed to be the same. It ignores the compounding effect of investment returns made in the...

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Calculating Weighted Average Mean

One characteristic of an arithmetic mean is that all observations have equal weight (=1/N). However, this may not always be the case. In some cases, different observations may influence the mean differently. This has special relevance in portfolios where a portfolio...

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Calculating Arithmetic Mean

Arithmetic mean is the simple average of all observations and is calculated by adding all the observations and dividing it by the total number of observations. We can calculate arithmetic mean for both the population and the sample. Population Mean This is the...

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Measures of Central Tendency

The measures of central tendency identify what is the center of a data set. These are the most widely used tools among all the statistical measures. The most commonly used measures of central tendency include: arithmetic mean, geometric mean, weighted average mean,...

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Properties of a Data Set (Histogram / Frequency Polygon)

Histogram The data in a frequency distribution can be presented using a histogram. A histogram is a bar chart with different intervals on the X-axis and the absolute frequencies on the Y-axis. The histogram for our data is presented below: Frequency Polygon A...

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Relative Frequencies and Cumulative Relative Frequencies

The data in a frequency distribution can also be presented using relative frequencies. Once we have relative frequencies, we can calculate cumulative relative frequencies where as we move from first frequency interval to the last, we keep adding the relative...

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Parameter, Sample Statistic, and Frequency Distribution

Earlier we took an example of measuring the average savings for a group of 100 families. This data of 100 families represents the population. The properties of a population such as mean and standard deviation are called parameters. Instead if we wanted to measure the...

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Types of Measurement Scales

Depending on the information we want the data to represent, we can choose one of the four measurement scales. Nominal Scale Used to classify data Observations are put into categories based on some criteria. The category labels can be numbers but they don’t have any...

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