Her time, 11.1, is still in the first quartile. When the two outliers are removed, Sandra can see that most of the data is grouped closely together. She recalculates her statistical measures and creates a new box-and-whisker plot: Sandra believes that neither Teresa nor Lisa’s scores are useful in gauging her speed. Another teammate, Lisa, had fallen during the race but got up and continued to the finish line. She knows that her friend, Teresa, is fast with a time of 10.1. When Sandra analyzes the box-and-whisker plot, she finds that her time, 11.1 seconds, is barely less than the first quartile. She finally draws whiskers from the quartiles to the extremes. She places the extremes, 10.1 and 19.6, on the numbers with points. Then, she draws boxes between the quartiles and the median. Then, she finds the first and third quartiles and places these numbers on the number line. The 10 th and 11 th data values are both 11.6. Then, she finds the median and places this number on the number line. The extreme maximum is 19.6 and the extreme minimum is 10.1. Next, she draws a number line that includes the extremes. Sandra’s time was 11.1 and she wants to know how she compares to the rest of her team. They recently ran a 100 meter dash at a track meet and recorded official times. Take a look at how removing an outlier can affect the interpretation of the data. Sometimes when you consider data, you might choose to remove the outliers in order to draw better conclusions based on the data. When you discuss measures of central tendency like mean, median, and mode, you must also remember that in the real world there are many exceptions. Outliers are points that are unusually large or small compared to the rest of the data. Finally, the extreme minimum, 35, appears to be an outlier as the left whisker is very long compared to the rest of the plot. The extremes in this data set are approximately 35 and 129.Ĭ. The first quartile is approximately 82 and the third quartile approximately 104.ĭ. The interquartile range, then, is 104 – 82 or 22.Į. Use the given box-and-whisker plot to identify: a) the extremes, b) the median, c) the quartiles, d) the interquartile range, and e) the outliers (if any).Ī. If there isn’t a single point that is exceptionally far from other points, then an outlier doesn’t exist. It can be calculated by subtracting the first quartile from the third quartile.įinally, the outliers, data items that are far away from the general trend, can be located as extremes that cause the whiskers to be exceptionally long. This shows where the middle half of the data is located. The interquartile range is the range between the first quartile and the third quartile. The second and fourth points, between the median and the extremes, give the quartiles. The third or middle point gives the median of all the data. The first and last points give the extremes of the data. Boxes are then drawn between the quartiles and whiskers are drawn to the extremes.Ī box-and-whisker plot that is already constructed can quickly supply statistical measures by looking at the five points. Finally, use the smallest data value and the largest data value as the endpoints or extremes. The median of each half, the quartile, is then calculated. Use the median as the middle point on the box-and-whisker plot and to split the data in half. Then, create a number line that shows the range of the data using equal intervals. The smallest data point (the extreme minimum) and the largest data point (the extreme maximum) are also displayed on the graph.įirst, arrange the data in order from smallest to largest. The data are divided into four equal parts, separated by points called quartiles. A box-and-whisker plot is created by determining five points. Box-and-whisker plots display the distribution of data items along a number line. \)Īt times it is useful to get a general idea of how data clusters together.
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