Just like quartiles, percentiles and percentile rank are among the measures of position. Percentiles divide a ranked data (ordered set of data ) into 100 equal parts. 99 percentiles are needed to divide any data set into 100 equal parts. The data should be ranked in increasing order to compute percentiles. The kth percentile is […]
Quartiles and interquartile range are among the measures of position. Just like the name indicates, quartiles divide a ranked data (ordered set of data ) into four equal parts. Only three measures are needed to divide any data set into four equal parts. These three measures that will divide an ordered data set into four […]
Just like the Chebyshev’s theorem, the empirical rule can also be used to find the percentage of the total observations that fall within a given interval about the mean. Here is the empirical rule: An illustration is shown below: Notice that 34% + 34% = 68% and 34% + 34% + 13.5% + 13.5% = […]
Chebyshev’s theorem will show you how to use the mean and the standard deviation to find the percentage of the total observations that fall within a given interval about the mean. Chebyshev’s theorem For any number k greater than 1, at least of the data values lie k standard deviations of the mean. […]
The formula for variance and standard deviation for grouped data is very similar to the one for ungrouped data. Below, we show the formula for ungrouped data and grouped data. […]
The difference between parameter and statistic is simple. The mean, median, mode, range, variance, or standard deviation, or any other numerical measure is called a parameter when the data set represent the entire population. The mean, median, mode, range, variance, or standard deviation, or any other numerical measure is called a statistic when the data set is a […]
The standard deviation (SD) tells how far the values of a data set are from the mean. If the standard deviation is big, the values are, on average, far from the mean. On the other hand, if the standard deviation is small, the values are, on average, close to the mean. To see what we […]
Measures of dispersion, also called measures of variation, are measures that help us to know about the spread or variation of a data set. At this point, you may not quite understand what we mean by spread or variation. We will illustrate with an example. Suppose that “professor Johnson” teaches calculus 1 and “professor Peter” […]
You can find the mean from a frequency table when you don’t know the exact values in the classes. Suppose somebody conducted a survey to find out the number of cups of water drank daily by people. The person who conducted the survey interviewed 52 people and he gave you this frequency table in order […]
The relationship between the mean, median, and mode is shown with these 3 histograms. Symmetric histogram […]
What is the best measure of center? There is no single best answer to this question. The table below shows a comparison of mean, median, mode, and midrange. Measure of center (Average) Definition Does it exist? Takes every value into account? Affected by extreme values How often is it used? Mean Always exists […]
The midrange of a data set is the value between the biggest value and the lowest value. To find the midrange of a data set, just add the biggest value to the smallest value and then divide the sum by 2. Since you are just looking for the highest and lowest values, it is not […]
The mode of a data set is the value that occurs most frequently. In other words, you are looking for the value with the highest frequency. The following data set gives the number of hours kids spend on homework every night. 2 3 4 1 […]
The median of a set of data is the middle value after the data set has been ranked either in increasing or decreasing order. The symbol used for the median is . We pronounce as “x-tilde.” Since the median is the middle value, it divides a ranked data set into two equal parts. There are two […]
The arithmetic mean, also called mean or average, is the most frequently used measure of central tendency in statistics. You can only find the arithmetic mean for a quantitative data. To find it, use this formula Arithmetic mean = Symbols used for the mean It is important to see the difference between symbols […]
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