Modified Box-and-Whisker Plot In Exercises 59–62, (a) identify any outliers and (b) draw a modified box-and-whisker plot that represents the data set. Use asterisks (*) to identify outliers.


75 78 80 75 62 72 74 75 80 95 76 72

Verified step by step guidance

1. Step 1: Organize the data set in ascending order: {62, 72, 72, 74, 75, 75, 75, 76, 78, 80, 80, 95}.
2. Step 2: Calculate the five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. Use the formulas for Q1 and Q3 based on the position of the data points in the ordered set.
3. Step 3: Determine the interquartile range (IQR) using the formula IQR = Q3 - Q1. Then, calculate the lower and upper bounds for outliers using the formulas: Lower Bound = Q1 - 1.5 * IQR and Upper Bound = Q3 + 1.5 * IQR.
4. Step 4: Identify any data points that fall below the lower bound or above the upper bound. These points are considered outliers and should be marked with asterisks (*) in the modified box-and-whisker plot.
5. Step 5: Draw the modified box-and-whisker plot. Represent the five-number summary with a box and whiskers, and use asterisks (*) to indicate any outliers identified in Step 4.

Key Concepts

Outliers

Outliers are data points that significantly differ from other observations in a dataset. They can skew the results of statistical analyses and may indicate variability in measurement, experimental errors, or novel phenomena. In a box-and-whisker plot, outliers are typically identified as points that lie beyond 1.5 times the interquartile range (IQR) from the quartiles.

Box-and-Whisker Plot

A box-and-whisker plot is a graphical representation of a dataset that displays its central tendency and variability. It consists of a box that represents the interquartile range (IQR), with lines (whiskers) extending to the minimum and maximum values within 1.5 times the IQR. This plot helps visualize the distribution of data, including the median, quartiles, and potential outliers.

Interquartile Range (IQR)

The interquartile range (IQR) is a measure of statistical dispersion that represents the range within which the central 50% of the data lies. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). The IQR is crucial for identifying outliers and understanding the spread of the data, as it is less affected by extreme values than the overall range.