The data set represents the number of minutes a sample of 27 people exercise each week.
108 139 120 123 120 132 123 131 131
157 150 124 111 101 135 119 116 117
127 128 139 119 118 114 127 142 130

g. Display the data using a box-and-whisker plot.

검증된 단계별 안내

Step 1: Organize the data in ascending order. This will help in identifying the minimum, maximum, quartiles, and median values. The ordered data set is: 101, 108, 111, 114, 116, 117, 118, 119, 119, 120, 120, 123, 123, 124, 127, 127, 128, 130, 131, 131, 132, 135, 139, 139, 142, 150, 157.

Step 2: Identify the five-number summary for the data set. These include the minimum value, first quartile (Q1), median (Q2), third quartile (Q3), and maximum value. Use the following definitions: Q1 is the median of the lower half of the data (excluding the overall median), Q2 is the median of the entire data set, and Q3 is the median of the upper half of the data (excluding the overall median).

Step 3: Calculate the interquartile range (IQR) to identify potential outliers. The formula for IQR is:

IQR = Q3 - Q1

. Any data point below

Q1 - 1.5 \(\times\) IQR

or above

Q3 + 1.5 \(\times\) IQR

is considered an outlier.

Step 4: Draw a number line that includes the range of the data. Plot the five-number summary (minimum, Q1, median, Q3, and maximum) on the number line. Use vertical lines to represent Q1, Q2, and Q3, and connect them with a box. Extend whiskers from the box to the minimum and maximum values that are not outliers.

Step 5: If there are any outliers, mark them as individual points outside the whiskers. Label the box-and-whisker plot appropriately to ensure clarity and interpretability.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Box-and-Whisker Plot

A box-and-whisker plot, or box plot, is a graphical representation of a data set that displays its minimum, first quartile, median, third quartile, and maximum. The 'box' shows the interquartile range (IQR), which contains the middle 50% of the data, while the 'whiskers' extend to the smallest and largest values within 1.5 times the IQR from the quartiles. This plot is useful for visualizing the distribution, central tendency, and variability of the data.

Quartiles

Quartiles are values that divide a data set into four equal parts, each containing 25% of the data. The first quartile (Q1) is the median of the lower half of the data, the second quartile (Q2) is the overall median, and the third quartile (Q3) is the median of the upper half. Understanding quartiles is essential for constructing a box-and-whisker plot, as they help identify the spread and center of the data.

Interquartile Range (IQR)

The interquartile range (IQR) is a measure of statistical dispersion that represents the range between the first quartile (Q1) and the third quartile (Q3). It is calculated as IQR = Q3 - Q1 and indicates the spread of the middle 50% of the data. The IQR is particularly useful for identifying outliers and understanding the variability within a data set, making it a key component in the construction of box-and-whisker plots.

The data set represents the number of minutes a sample of 27 people exercise each week.108 139 120 123 120 132 123 131 131157 150 124 111 101 135 119 116 117127 128 139 119 118 114 127 142 130g. Display the data using a box-and-whisker plot.