#Box plot vs stem plot series

To calculate the standard deviation of a population, we would use the population mean, μ, and the formula σ = ∑ ( x − μ ) 2 N ∑ ( x − μ ) 2 N or σ = ∑ f ( x − μ ) 2 N ∑ f ( x − μ ) 2 N. s = ∑ ( x − x ¯ ) 2 n − 1 ∑ ( x − x ¯ ) 2 n − 1 or s = ∑ f ( x − x ¯ ) 2 n − 1 ∑ f ( x − x ¯ ) 2 n − 1 is the formula for calculating the standard deviation of a sample.The standard deviation allows us to compare individual data or classes to the data set mean numerically.There are different equations to use if you are calculating the standard deviation of a sample or of a population. The standard deviation can help you calculate the spread of data. A symmetrical distribution looks like Figure 2.18. A left (or negative) skewed distribution has a shape like Figure 2.20. A right (or positive) skewed distribution has a shape like Figure 2.19. Looking at the distribution of data can reveal a lot about the relationship between the mean, the median, and the mode. 2.6 Skewness and the Mean, Median, and Mode Divide the sum of these values by the total number of data values in the set. Multiply each midpoint by the number of values found in the corresponding range. However, the mean can be approximated if you add the lower boundary with the upper boundary and divide by two to find the midpoint of each interval. The mean, median, and mode are extremely helpful when you need to analyze your data, but if your data set consists of ranges that lack specific values, the mean may seem impossible to calculate. The mode will tell you the most frequently occurring datum (or data) in your 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 mean and the median can be calculated to help you find the center of a data set. Once the box plot is graphed, you can display and compare distributions of data. Before a box plot can be graphed, the following data points must be calculated: the minimum value, the first quartile, the median, the third quartile, and the maximum value. The IQR is found by subtracting Q 1 from Q 3 and can help determine outliers by using the following two expressions.īox plots are a type of graph that can help visually organize data. The interquartile range, or IQR, is the range of the middle 50 percent of the data values. The first quartile ( Q 1) is the 25 th percentile, the second quartile ( Q 2 or median) is the 50 th percentile, and the third quartile ( Q 3) is the 75 th percentile. For example, an observation at the 50 th percentile would be greater than 50 percent of the other observations in the set. Percentiles are used to compare and interpret data. The values that divide a rank-ordered set of data into 100 equal parts are called percentiles.

#Box plot vs stem plot series

Time series graphs can be helpful when looking at large amounts of data for one variable over a period of time. The data usually go on the y-axis with the frequency being graphed on the x-axis. A frequency polygon can also be used when graphing large data sets with data points that repeat. Histograms are typically used for large, continuous, quantitative data sets. The heights of the bars correspond to frequency values.

The horizontal scale represents classes of quantitative data values, and the vertical scale represents frequencies. The graph consists of bars of equal width drawn adjacent to each other. 2.2 Histograms, Frequency Polygons, and Time Series GraphsĪ histogram is a graphic version of a frequency distribution. Bar graphs are especially useful when categorical data are being used. One axis of the chart shows the specific categories being compared, and the other axis represents a discrete value. A bar graph is a chart that uses either horizontal or vertical bars to show comparisons among categories. These graphs are useful for finding trends, that is, finding a general pattern in data sets, including temperature, sales, employment, company profit, or cost, over a period of time. A line graph is often used to represent a set of data values in which a quantity varies with time. The advantage in a stem-and-leaf plot is that all values are listed, unlike a histogram, which gives classes of data values. In a stem-and-leaf plot, all data values within a class are visible. 2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar GraphsĪ stem-and-leaf plot is a way to plot data and look at the distribution.