![]() the salaries at Welsh Bank and Bank of Finland are equally consistent (since the interquartile range, £18,000, is the same for both.Therefore, people earn more on average at the Bank of Finland than at Welsh Bank. the median salary is higher at the Bank of Finland ( £62,000 compared to £52,000).The 75 th value for Welsh Bank corresponds to a salary of £61,000, and the 75 th value for The Bank of Finland corresponds to a salary of £68,000.Īs a result, the completed box plots should be similar to the two below:ī) By comparing the two box plots, we can see that: On the cumulative frequency graph, we need to locate 75 on the cumulative frequency axis and find the corresponding salary. We have the smallest value ( 220) and the largest value ( 400), so we will have to work out the remaining values. There are two potential outliers in distribution A.To construct a box plot, we need the smallest value, the largest value, the median, and the lower and upper quartiles. According to the definition used by the function in R software, all values higher than Q3 + 1.5 x (Q3 - Q1) = 0.32 + 1.5 x 0.30 = 0.77 are outside the right whisker and indicated by a circle. The horizontal line inside the box is the median. Therefore the vertical width of the central box represents the inter-quartile deviation. The bottom side of the box represents the first quartile, and the top side, the third quartile. The interquartile range is Q3 - Q1 = 0.32 – 0.02 = 0.30. The interquartile range (IQR) is a measure of statistical dispersion that is based on dividing a data set into quartiles. The box plot is also referred to as box and whisker plot or box and whisker diagram. The distribution C is negatively skewed because the whisker and half-box are longer on the left side of the median than on the right side.Īll three distributions include potential outliers. The centre of distribution C is the highest of the three distributions (median is 0.88).It’s the most concentrated distribution because the interquartile range is 0.21, compared to 0.30 for distribution A and 0.26 for distribution C. The length of the box is the difference between these two percentiles and is called the interquartile range (IQR). Distribution B is approximately symmetric, because both half-boxes are almost the same length (0.11 on the left side and 0.10 on the right side).The distribution is positively skewed, because the whisker and half-box are longer on the right side of the median than on the left side. The centre of distribution A is the lowest of the three distributions (median is 0.11).The information is grouped by Measurement (appearing as row headers), Distribution A, Distribution B and Distribution C (appearing as column headers). This table displays the results of Data table for chart 4.5.2.1. Example 1 – Comparison of three box and whisker plots Data points that are outside this interval are represented as points on the graph and considered potential outliers. That is, the whisker reaches the value that is the furthest from the centre while still being inside a distance of 1.5 times the interquartile range from the lower or upper quartile. The box and whisker plot can be presented horizontally, like in figure 4.5.2.1, or vertically.Ī variation of the box and whisker plot restricts the length of the whiskers to a maximum of 1.5 times the interquartile range.The graph is usually presented with an axis that indicates the values (not shown on figure 4.5.2.1).The whiskers are the two lines outside the box, that go from the minimum to the lower quartile (the start of the box) and then from the upper quartile (the end of the box) to the maximum.Sometimes, the mean is also indicated by a dot or a cross on the box plot. The vertical line that split the box in two is the median.The box covers the interquartile interval, where 50% of the data is found. The left and right sides of the box are the lower and upper quartiles.The figure shows the shape of a box and whisker plot and the position of the minimum, lower quartile, median, upper quartile and maximum. A box plot is ideal for comparing distributions because the centre, spread and overall range are immediately apparent.įigure 4.5.2.1 shows how to build the box and whisker plot from the five-number summary. It doesn’t show the distribution in as much detail as histogram does, but it’s especially useful for indicating whether a distribution is skewed and whether there are potential unusual observations (outliers) in the data set. The box and whisker plot, sometimes simply called the box plot, is a type of graph that help visualize the five-number summary.
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