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Which part? To be solved?
User:
A,B,CAnswer:
All the answers given below:Step-by-step explanation:
Step 5:
A
To construct a box-and-whisker plot of the given wait times for the 11 volunteers, we need to arrange the data in ascending order. Here is the sorted list of wait times:
0, 5, 25, 46, 55, 70, 85, 103, 113, 120, 140
Now, let's construct the box-and-whisker plot using the following steps:
Step 1: Find the minimum and maximum values. The minimum value is 0, and the maximum value is 140.
Step 2: Find the median. The median is the middle value of the dataset. Since we have 11 data points, the median will be the 6th value, which is 70.
Step 3: Find the lower quartile (Q1). The lower quartile is the median of the lower half of the dataset. We have 5 data points in the lower half, so the lower quartile will be the median of these 5 values. The median of the lower half is the average of the 3rd and 4th values, which are 25 and 46. So, Q1 = (25 + 46) / 2 = 35.5.
Step 4: Find the upper quartile (Q3). The upper quartile is the median of the upper half of the dataset. We have 5 data points in the upper half, so the upper quartile will be the median of these 5 values. The median of the upper half is the average of the 8th and 9th values, which are 103 and 113. So, Q3 = (103 + 113) / 2 = 108.
Step 5: Calculate the interquartile range (IQR). The interquartile range is the difference between Q3 and Q1. IQR = Q3 - Q1 = 108 - 35.5 = 72.5.
Step 6: Draw the box-and-whisker plot. Using the minimum, Q1, median, Q3, and maximum values, we can draw the box-and-whisker plot as follows:
Here the line at 70 is showing the median of the given data.
B
Possible data is:
60, 150, 100, 130, 120, 70, 80, 90, 140, 110, 140
C
a. Comparing the shape of the two box-and-whisker plots: Unfortunately, without the exact box-and-whisker plots, I cannot provide a visual comparison of the shapes. However, you can compare the spread and symmetry of the two plots using the criteria mentioned earlier. Look at the lengths of the whiskers and the interquartile range (IQR) to assess the spread. Additionally, examine the position of the median to evaluate symmetry.
b. Identifying outliers in either data set: To identify outliers, we can examine the positioning of individual data points outside the whiskers in each box-and-whisker plot. Outliers are typically considered values that are significantly higher or lower than the rest of the data. Please check if there are any values in either data set that fall outside the whiskers.
c. Determining the most appropriate measure of central tendency: To determine the most appropriate measure of central tendency (mean, median, or mode) for each data set, consider the characteristics of the data. Assess the presence of skewness, outliers, and the nature of the data to guide your decision.