1. What are the minimum, first quartile, median, third quartile, and maximum of the data set?
18, 20, 11, 10, 8, 6, 12, 4
A: Minimum: 4; First Quartile: 7; Median: 10.5; Third Quartile: 17.5; Maximum: 20
B: Minimum: 4; First Quartile: 5.5; Median: 12.75; Third Quartile: 15; Maximum: 20<~~(MA)
C: Minimum: 4; First Quartile: 8.75; Median: 12.75; Third Quartile: 17.5; Maximum: 20
D: Minimum: 4; First Quartile: 7; Median: 10.5; Third Quartile: 15; Maximum: 20
<~~(MA) = My Answer
arrange in order ... 4 , 6 , 8 , 10 , 11 , 12 , 18 , 20
8 values , so two per quartile
the quartile "boundries" are the average of the numbers on either side
... 6 is the last value in the 1st quartile , 8 is the 1st value in the 2nd quartile
... so the 1st quartile is delineated by 7 ... (8 + 6) / 2
take another look at the answers
then is it C?
To find the minimum, first quartile, median, third quartile, and maximum of the data set, you can follow these steps:
1. Sort the data set in ascending order: 4, 6, 8, 10, 11, 12, 18, 20.
2. Find the minimum, which is the smallest value in the sorted data set. In this case, the minimum is 4.
3. Find the first quartile (Q1), which is the median of the lower half of the data set. In this case, the lower half is {4, 6, 8, 10}. Since there are four values, the median is the average of the two middle values, which is (6 + 8) / 2 = 7.
4. Find the median, which is the middle value of the entire data set. In this case, the median is 10.
5. Find the third quartile (Q3), which is the median of the upper half of the data set. In this case, the upper half is {11, 12, 18, 20}. Since there are four values, the median is the average of the two middle values, which is (12 + 18) / 2 = 15.
6. Find the maximum, which is the largest value in the sorted data set. In this case, the maximum is 20.
Based on these steps, the answer is B: Minimum: 4; First Quartile: 5.5; Median: 12.75; Third Quartile: 15; Maximum: 20.
To find the minimum, first quartile, median, third quartile, and maximum of a data set, we need to understand some basic concepts in statistics.
1. Minimum: The minimum is the smallest value in the data set. In this case, the smallest value is 4.
2. Median: The median is the middle value when the data set is arranged in numerical order. If there is an odd number of values, the median is the exact middle value. If there is an even number of values, the median is the average of the two middle values. To find the median of this data set, we first need to arrange the numbers in order: 4, 6, 8, 10, 11, 12, 18, 20. Since there are 8 values, we take the average of the 4th and 5th values, which are 10 and 11. Therefore, the median is (10 + 11) / 2 = 21 / 2 = 10.5.
3. Quartiles: Quartiles divide a data set into four equal parts. The first quartile (Q1) is the value below which 25% of the data falls. The third quartile (Q3) is the value below which 75% of the data falls.
To find the quartiles, we need to calculate the positions of the first quartile (Q1) and third quartile (Q3). Since we have 8 values, we can use the following formulas:
Q1 = (n + 1) / 4
Q3 = 3(n + 1) / 4
where n is the number of values in the data set.
For this data set, Q1 = (8 + 1) / 4 = 9 / 4 = 2.25. We round this down to the 2nd value, which is 6. Therefore, the first quartile is 6.
Q3 = 3(8 + 1) / 4 = 27 / 4 = 6.75. We round this number up to the 7th value, which is 18. Therefore, the third quartile is 18.
4. Maximum: The maximum is the largest value in the data set. In this case, the largest value is 20.
Using the above information, we can determine the correct answer:
B: Minimum: 4; First Quartile: 5.5; Median: 12.75; Third Quartile: 15; Maximum: 20 (My Answer)