This makes sense, the median is the average of the middle two numbers.Ħ. You can verify this number by using the QUARTILE.EXC function or looking at the box and whisker plot.ĥ. In this example, n = 8 (number of data points).Ĥ. This function interpolates between two values to calculate a quartile. For example, select the even number of data points below.Įxplanation: Excel uses the QUARTILE.EXC function to calculate the 1st quartile (Q 1), 2nd quartile (Q 2 or median) and 3rd quartile (Q 3). Most of the time, you can cannot easily determine the 1st quartile and 3rd quartile without performing calculations.ġ. As a result, the whiskers extend to the minimum value (2) and maximum value (34). As a result, the top whisker extends to the largest value (18) within this range.Įxplanation: all data points are between -17.5 and 34.5. Therefore, in this example, 35 is considered an outlier. A data point is considered an outlier if it exceeds a distance of 1.5 times the IQR below the 1st quartile (Q 1 - 1.5 * IQR = 2 - 1.5 * 13 = -17.5) or 1.5 times the IQR above the 3rd quartile (Q 3 + 1.5 * IQR = 15 + 1.5 * 13 = 34.5). In this example, IQR = Q 3 - Q 1 = 15 - 2 = 13. On the Insert tab, in the Charts group, click the Statistic Chart symbol.Įxplanation: the interquartile range (IQR) is defined as the distance between the 1st quartile and the 3rd quartile. This means that there is more variability in the middle 50% of the first data set.2. The IQR for the first data set is greater than the IQR for the second set. The first data set has the wider spread for the middle 50% of the data. Which box plot has the widest spread for the middle 50% of the data (the data between the first and third quartiles)? What does this mean for that set of data in comparison to the other set of data?.Create a box plot for each set of data.Find the smallest and largest values, the median, and the first and third quartile for the night class.Find the smallest and largest values, the median, and the first and third quartile for the day class.The middle 50% (middle half) of the data has a range of 5.5 inches.The interval 59–65 has more than 25% of the data so it has more data in it than the interval 66 through 70 which has 25% of the data.Range = maximum value – the minimum value = 77 – 59 = 18.So, the second quarter has the smallest spread and the fourth quarter has the largest spread. The spreads of the four quarters are 64.5 – 59 = 5.5 (first quarter), 66 – 64.5 = 1.5 (second quarter), 70 – 66 = 4 (third quarter), and 77 – 70 = 7 (fourth quarter).Each quarter has approximately 25% of the data.The following data are the heights of 40 students in a statistics class.ĥ9 60 61 62 62 63 63 64 64 64 65 65 65 65 65 65 65 65 65 66 66 67 67 68 68 69 70 70 70 70 70 71 71 72 72 73 74 74 75 77Ĭonstruct a box plot with the following properties the calculator instructions for the minimum and maximum values as well as the quartiles follow the example. The box plot gives a good, quick picture of the data. The median or second quartile can be between the first and third quartiles, or it can be one, or the other, or both. The “whiskers” extend from the ends of the box to the smallest and largest data values. Approximately the middle 50 percent of the data fall inside the box. The first quartile marks one end of the box and the third quartile marks the other end of the box. The smallest and largest data values label the endpoints of the axis. To construct a box plot, use a horizontal or vertical number line and a rectangular box. We use these values to compare how close other data values are to them. A box plot is constructed from five values: the minimum value, the first quartile (Q 1), the median (Q 2), the third quartile (Q 3), and the maximum value. They also show how far the extreme values are from most of the data. \)īox plots (also called box-and-whisker plots or box-whisker plots) give a good graphical image of the concentration of the data.
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