Five Number Summary And Box And Whisker Plot

The median of a data set is the middle value when the data is arranged in ascending or descending order. In this case, the box and whisker plot shows that the median is represented by the line inside the box, which is located at the value of 30. Therefore, the median of the data is 30.

The range of the data can be determined by subtracting the smallest value from the largest value. In this case, the largest value on the box and whisker plot is 42 and the smallest value is not visible on the plot. Therefore, the range of the data is 42.

The IQR (Interquartile Range) is a measure of statistical dispersion, specifically the range between the first quartile (Q1) and the third quartile (Q3) of a dataset. In this case, since the answer is 25, it means that the range between Q1 and Q3 is 25 units.

The 5 number summary consists of the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value of the data set. In this case, the minimum value is 0, the first quartile is 5, the median is 15, the third quartile is 25, and the maximum value is 30. Therefore, the correct answer is 0, 5, 15, 25, 30.

The median is the middle value of a set of data when arranged in ascending order. In this case, the data listed in ascending order is 25, 34, 46, 48, 53, 55, 63, 67, 72, 72, 77, 88. The median is the average of the two middle values, which are 55 and 63. Therefore, there are 6 values (72, 72, 77, 88) that are higher than the median, out of a total of 12 values. So, the percentage of data higher than the median is 6/12 or 50%.

The interquartile range is a measure of the spread of the middle 50% of the data. To find it, we first need to arrange the data in ascending order: 0, 5, 5, 10, 15, 15, 20, 20, 25, 25, 30. The lower quartile (Q1) is the median of the lower half of the data, which is 10. The upper quartile (Q3) is the median of the upper half of the data, which is 25. The interquartile range is then calculated by subtracting Q1 from Q3: 25 - 10 = 15. Therefore, the correct answer is 15.

The 5 number summary provides a summary of the distribution of the data. It consists of the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value. In this case, the minimum value is 30, the first quartile is 50, the median is 75, the third quartile is 100, and the maximum value is 150.

The upper quartile is the median of the upper half of the data. To find the upper quartile, we first need to arrange the data in ascending order: 25, 34, 46, 48, 53, 55, 63, 67, 72, 72, 77, 88. The upper half of the data is 63, 67, 72, 72, 77, 88. Since there are 6 numbers in the upper half and only 1 number (88) is higher than the upper quartile, the percentage of data higher than the upper quartile is 1/6 or approximately 16.7%. Therefore, the correct answer is 25%, which is the closest option to 16.7%.

The lower quartile is the median of the lower half of the data. In this case, the lower quartile is 48. Out of the 12 data points listed, there are 9 data points (72, 67, 63, 55, 72, 77) that are higher than 48. Therefore, the percentage of the data that is higher than the lower quartile is 9/12 = 75%.

To find the interquartile range (IQR) of the given data, follow these steps:

Order the data: 30, 50, 50, 90, 100, 150

Find the median (Q2):

There are 6 data points, so the median is the average of the 3rd and 4th values:

Median = (50 + 90) / 2 = 70

Find the lower quartile (Q1):

Q1 is the median of the first half of the data (30, 50, 50):

Q1 = 50 (middle value of the first three numbers)

Find the upper quartile (Q3):

Q3 is the median of the second half of the data (90, 100, 150):

Q3 = 100 (middle value of the last three numbers)

Calculate the IQR:

IQR = Q3 - Q1

IQR = 100 - 50 = 50