It seems like you have provided two sets of data. I assume that the first set is a dataset of 11, 9, 8, 7, 12, and 6, and the second set is a dataset of 13, 14, 10, 11, 9, 11, 14, 15, and 16.
To find the values of Q1, Q2, Q3, D4, Dε, D8, P25, P39, P75, and P88, we need to first order the data from smallest to largest.
For the first set of data:
6, 7, 8, 9, 11, 12
Q1: The median of the lower half of the dataset, which is {6, 7, 8}. Q1 = 7.
Q2: The median of the entire dataset, which is {6, 7, 8, 9, 11, 12}. Q2 = 8.5.
Q3: The median of the upper half of the dataset, which is {9, 11, 12}. Q3 = 11.
D4: The fourth decile, which is the value that splits the dataset into 4 equal parts. There are 6 values, so each part contains 6/4 = 1.5 values. The fourth decile falls in between the second and third values, which are 7 and 8. D4 = (7+8)/2 = 7.5.
Dε: The value that is closest to the mean of the dataset, which is (6+7+8+9+11+12)/6 = 8.83. The value closest to 8.83 is 9. Dε = 9.
D8: The eighth decile, which is the value that splits the dataset into 8 equal parts. There are 6 values, so each part contains 6/8 = 0.75 values. The eighth decile falls in between the fifth and sixth values, which are 11 and 12. D8 = (11+12)/2 = 11.5.
For the second set of data:
9, 10, 11, 11, 13, 14, 14, 15, 16
Q1: The median of the lower half of the dataset, which is {9, 10, 11}. Q1 = 10.
Q2: The median of the entire dataset, which is {9, 10, 11, 11, 13, 14, 14, 15, 16}. Q2 = 13.
Q3: The median of the upper half of the dataset, which is {13, 14, 14, 15, 16}. Q3 = 14.
D4: The fourth decile, which is the value that splits the dataset into 4 equal parts. There are 9 values, so each part contains 9/4 = 2.25 values. The fourth decile falls in between the second and third values, which are 10 and 11. D4 = (10+11)/2 = 10.5.
Dε: The value that is closest to the mean of the dataset, which is (9+10+11+11+13+14+14+15+16)/9 = 12. Dε = 13.
D8: The eighth decile, which is the value that splits the dataset into 8 equal parts. There
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Answer:
It seems like you have provided two sets of data. I assume that the first set is a dataset of 11, 9, 8, 7, 12, and 6, and the second set is a dataset of 13, 14, 10, 11, 9, 11, 14, 15, and 16.
To find the values of Q1, Q2, Q3, D4, Dε, D8, P25, P39, P75, and P88, we need to first order the data from smallest to largest.
For the first set of data:
6, 7, 8, 9, 11, 12
Q1: The median of the lower half of the dataset, which is {6, 7, 8}. Q1 = 7.
Q2: The median of the entire dataset, which is {6, 7, 8, 9, 11, 12}. Q2 = 8.5.
Q3: The median of the upper half of the dataset, which is {9, 11, 12}. Q3 = 11.
D4: The fourth decile, which is the value that splits the dataset into 4 equal parts. There are 6 values, so each part contains 6/4 = 1.5 values. The fourth decile falls in between the second and third values, which are 7 and 8. D4 = (7+8)/2 = 7.5.
Dε: The value that is closest to the mean of the dataset, which is (6+7+8+9+11+12)/6 = 8.83. The value closest to 8.83 is 9. Dε = 9.
D8: The eighth decile, which is the value that splits the dataset into 8 equal parts. There are 6 values, so each part contains 6/8 = 0.75 values. The eighth decile falls in between the fifth and sixth values, which are 11 and 12. D8 = (11+12)/2 = 11.5.
For the second set of data:
9, 10, 11, 11, 13, 14, 14, 15, 16
Q1: The median of the lower half of the dataset, which is {9, 10, 11}. Q1 = 10.
Q2: The median of the entire dataset, which is {9, 10, 11, 11, 13, 14, 14, 15, 16}. Q2 = 13.
Q3: The median of the upper half of the dataset, which is {13, 14, 14, 15, 16}. Q3 = 14.
D4: The fourth decile, which is the value that splits the dataset into 4 equal parts. There are 9 values, so each part contains 9/4 = 2.25 values. The fourth decile falls in between the second and third values, which are 10 and 11. D4 = (10+11)/2 = 10.5.
Dε: The value that is closest to the mean of the dataset, which is (9+10+11+11+13+14+14+15+16)/9 = 12. Dε = 13.
D8: The eighth decile, which is the value that splits the dataset into 8 equal parts. There
Answer:
To find Q1, Q2, Q3, we need to first order the dataset from smallest to largest:
8, 6, 9, 11, 13, 14, 15, 16, 712, 1114
Q1 (first quartile): The median of the lower half of the dataset.
Lower half of the dataset: 8, 6, 9, 11
Median of lower half: (6 + 8) / 2 = 7
Therefore, Q1 = 7
Q2 (second quartile): The median of the entire dataset.
Median of entire dataset: (9 + 11) / 2 = 10
Therefore, Q2 = 10
Q3 (third quartile): The median of the upper half of the dataset.
Upper half of the dataset: 13, 14, 15, 16, 712, 1114
Median of upper half: (15 + 16) / 2 = 15.5
Therefore, Q3 = 15.5
To find D4, D6, D8, we need to first calculate the interquartile range (IQR):
IQR = Q3 - Q1 = 15.5 - 7 = 8.5
D4 (fourth decile): The value that divides the dataset into 4 equal parts, with 40% of the data below it.
40% of the dataset is (0.4) * 10 = 4, so we need to find the value at index 4 in the ordered dataset.
D4 = 11
D6 (sixth decile): The value that divides the dataset into 10 equal parts, with 60% of the data below it.
60% of the dataset is (0.6) * 10 = 6, so we need to find the value at index 6 in the ordered dataset.
D6 = 14
D8 (eighth decile): The value that divides the dataset into 10 equal parts, with 80% of the data below it.
80% of the dataset is (0.8) * 10 = 8, so we need to find the value at index 8 in the ordered dataset.
D8 = 1114
To find P25, P39, P75, P88, we can use the same method as above:
P25 (25th percentile): The value that divides the dataset into 4 equal parts, with 25% of the data below it.
25% of the dataset is (0.25) * 10 = 2.5, so we need to interpolate between the values at indices 2 and 3 in the ordered dataset.
P25 = 8 + (2.5 - 2) * (9 - 8) = 8.5
P39 (39th percentile): The value that divides the dataset into 10 equal parts, with 39% of the data below it.
39% of the dataset is (0.39) * 10 = 3.9, so we need to interpolate between the values at indices 3 and 4 in the ordered dataset.
P39 = 9 + (3.9 - 3) * (11 - 9) = 9.78
P75 (75th percentile): The value that divides the dataset into 4 equal parts, with 75% of the data below it.
75% of the dataset is (0.75) * 10 = 7.5, so we need to interpolate between the values at indices 7 and 8 in the ordered