Answer:
To find the five-number summary of a data set, we need to find the minimum value, the first quartile (Q1), the median, the third quartile (Q3), and the maximum value.
We can first put the data set in order from smallest to largest:
14, 17, 19, 23, 25, 28, 30, 34, 40, 43
The minimum value is 14, and the maximum value is 43.
To find the median, we need to find the middle value. Since there are 10 numbers in the data set, the median is the average of the fifth and sixth values:
Median = (25 + 28) / 2 = 26.5
To find the first and third quartiles, we can use the median as a reference point. The first quartile (Q1) is the median of the lower half of the data set, and the third quartile (Q3) is the median of the upper half of the data set.
The lower half of the data set consists of the first five values:
14, 17, 19, 23, 25
The median of these values is:
Q1 = (19 + 23) / 2 = 21
The upper half of the data set consists of the last five values:
28, 30, 34, 40, 43
The median of these values is:
Q3 = (34 + 40) / 2 = 37
Therefore, the five-number summary for this data set is:
Minimum = 14
Q1 = 21
Median = 26.5
Q3 = 37
Maximum = 43
Looking at the answer choices, we can see that option C is the correct answer:
OA. 14, 19, 29, 34, 43
B. 14, 23, 26.5, 30, 43
C. 14, 19, 26.5, 34, 43
OD. 14, 23, 29, 30, 43