Question

Calculate the five-number summary of the given data. Use the approximation method. 18, 5, 14, 4, 10, 7, 13, 4, 4, 23, 20, 7, 23, 5, 10.

Answer 1

The five-number summary for the provided data set is Min = 4, Q1 = 5, Median = 10, Q3 = 19, and Max = 23. These values are determined by arranging the data in ascending order and then finding the minimum, first quartile, median, third quartile, and maximum values.

Step-by-step explanation:

To calculate the five-number summary of the given data set (18, 5, 14, 4, 10, 7, 13, 4, 4, 23, 20, 7, 23, 5, 10), we will follow these steps:

1. First, we need to arrange the data in ascending order: 4, 4, 4, 5, 5, 7, 7, 10, 10, 13, 14, 18, 20, 23, 23.
2. The minimum value (Min) is the smallest number, which is 4.
3. The maximum value (Max) is the largest number, which is 23.
4. The median (Med), or second quartile (Q2), is the middle value, which in this case is 10 (since there are 15 numbers, the median is the 8th number).
5. The first quartile (Q1) is the median of the first half of the data, excluding the median of the whole set if it is part of the data. The first half is 4, 4, 4, 5, 5, 7, 7. The median of this half is 5.
6. The third quartile (Q3) is the median of the second half of the data, excluding the median of the whole set if it is part of the data. The second half is 13, 14, 18, 20, 23, 23. The median of this half is 19 (the average of 18 and 20).

Therefore, the five-number summary is: Min = 4, Q1 = 5, Med = 10, Q3 = 19, Max = 23.