3: Numerical Summaries of Data
- Page ID
- 130235
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- 3.1: Measures of the Center of the Data
- The mean and the median can be calculated to help you find the "center" of a data set. The mean is the best estimate for the actual data set, but the median is the best measurement when a data set contains several outliers or extreme values. The mode will tell you the most frequently occurring datum (or data) in your data set. The mean, median, and mode are extremely helpful when you need to analyze your data.
- 3.2: Skewness and the Mean, Median, and Mode
- Looking at the distribution of data can reveal a lot about the relationship between the mean, the median, and the mode. There are three types of distributions. A right (or positive) skewed distribution, a left (or negative) skewed distribution and a symmetrical distribution.
- 3.3: Measures of the Spread of the Data
- An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard deviation. The standard deviation is a number that measures how far data values are from their mean.
- 3.4: The Empirical Rule and Chebyshev's Theorem
- The Empirical Rule is an approximation that applies only to data sets with a bell-shaped relative frequency histogram. It estimates the proportion of the measurements that lie within one, two, and three standard deviations of the mean. Chebyshev’s Theorem is a fact that applies to all possible data sets. It describes the minimum proportion of the measurements that lie must within one, two, or more standard deviations of the mean.
- 3.5: Measures of the Location of the Data
- The values that divide a rank-ordered set of data into 100 equal parts are called percentiles and are used to compare and interpret data. For example, an observation at the 50th percentile would be greater than 50 % of the other obeservations in the set. Quartiles divide data into quarters. The first quartile is the 25th percentile, the second quartile is 50th percentile, and the third quartile is the the 75th percentile. The interquartile range is the range of the middle 50 % of the data values
- 3.6: Box Plots
- Box plots are a type of graph that can help visually organize data. To graph a box plot the following data points must be calculated: the minimum value, the first quartile, the median, the third quartile, and the maximum value. Once the box plot is graphed, you can display and compare distributions of data.