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70 79 82 90 96 110 120 134 139 142 148 150 152 155 161 the IQR is 60 but show work on how to get 60
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20 30 32 16 31 32 13 20 28 32 15 18 20 21 32
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20 30 32 16 31 32 13 20 28 32 15 18 20 21 32 find the medien
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115 115 120 122 125 127 128 131 132 128 126 140 find Q1 Q2 and Q3
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1 4 6 7 9 10 10 11 12 12 14 15 17 18 19 find the MAD
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1 4 6 7 9 10 10 11 12 12 14 15 17 18 19 find the IQR
Answered by GPT 3.5
To find the interquartile range (IQR), you first need to find the first quartile (Q1) and the third quartile (Q3).

Step 1: Arrange the data in ascending order
70, 79, 82, 90, 96, 110, 120, 134, 139, 142, 148, 150, 152, 155, 161

Step 2: Calculate the median (Q2)
Since there are 15 numbers in the data set, the median is the middle number, which is 120.

Step 3: Calculate Q1
To find Q1, you need to find the median of the lower half of the data set. In this case, the lower half of the data set is: 70, 79, 82, 90, 96, 110
Median of the lower half = (82 + 90) / 2 = 86

Step 4: Calculate Q3
To find Q3, you need to find the median of the upper half of the data set. In this case, the upper half of the data set is: 134, 139, 142, 148, 150, 152, 155, 161
Median of the upper half = (148 + 150) / 2 = 149

Step 5: Calculate the IQR
IQR = Q3 - Q1
IQR = 149 - 86 = 63

Therefore, the interquartile range (IQR) of the data set is 63.
Answered by GPT 3.5
To find the interquartile range (IQR) for the data set {13, 15, 16, 18, 20, 20, 20, 21, 28, 30, 31, 32, 32, 32, 32}, we need to follow these steps:

Step 1: Arrange the data in ascending order
13, 15, 16, 18, 20, 20, 20, 21, 28, 30, 31, 32, 32, 32, 32

Step 2: Calculate the median (Q2)
Since there are 15 numbers in the data set, the median is the middle number, which is 20.

Step 3: Calculate Q1
To find Q1, you need to find the median of the lower half of the data set. In this case, the lower half of the data set is: 13, 15, 16, 18, 20
Median of the lower half = (15 + 16) / 2 = 15.5

Step 4: Calculate Q3
To find Q3, you need to find the median of the upper half of the data set. In this case, the upper half of the data set is: 28, 30, 31, 32, 32, 32, 32
Median of the upper half = (31 + 32) / 2 = 31.5

Step 5: Calculate the IQR
IQR = Q3 - Q1
IQR = 31.5 - 15.5 = 16

Therefore, the interquartile range (IQR) of the data set is 16.
Answered by GPT 3.5
To find the median of the data set {13, 15, 16, 18, 20, 20, 20, 21, 28, 30, 31, 32, 32, 32, 32}, we first need to arrange the data in ascending order:

13, 15, 16, 18, 20, 20, 20, 21, 28, 30, 31, 32, 32, 32, 32

Since there are 15 numbers in the data set, the median will be the middle number when the data is arranged in ascending order. In this case, the middle number or numbers are 20 and 20.

Therefore, the median of the data set is 20.
Answered by GPT 3.5
To find the first quartile (Q1), the second quartile (Q2), and the third quartile (Q3) for the data set {115, 115, 120, 122, 125, 127, 128, 131, 132, 128, 126, 140}, we need to follow these steps:

Step 1: Arrange the data in ascending order:
115, 115, 120, 122, 125, 126, 127, 128, 128, 131, 132, 140

Step 2: Calculate Q2 (Median):
Since there are 12 numbers in the data set, the median (Q2) is the average of the sixth and seventh terms.
Median = (126 + 127) / 2 = 126.5

Step 3: Calculate Q1:
To find Q1, you need to find the median of the lower half of the data set. In this case, the lower half of the data set is: 115, 115, 120, 122, 125, 126
Median of the lower half = (120 + 122) / 2 = 121

Step 4: Calculate Q3:
To find Q3, you need to find the median of the upper half of the data set. In this case, the upper half of the data set is: 128, 128, 131, 132, 140
Median of the upper half = (128 + 131) / 2 = 129.5

Therefore,
Q1 = 121
Q2 = 126.5
Q3 = 129.5
Answered by GPT 3.5
To find the Mean Absolute Deviation (MAD) for the data set {1, 4, 6, 7, 9, 10, 10, 11, 12, 12, 14, 15, 17, 18, 19}, follow these steps:

Step 1: Calculate the mean of the data set
Mean = (1 + 4 + 6 + 7 + 9 + 10 + 10 + 11 + 12 + 12 + 14 + 15 + 17 + 18 + 19) / 15
Mean = 140 / 15
Mean = 9.33 (rounded to two decimal places)

Step 2: Find the absolute deviations from the mean for each data point
|1 - 9.33| = 8.33
|4 - 9.33| = 5.33
|6 - 9.33| = 3.33
|7 - 9.33| = 2.33
|9 - 9.33| = 0.67
|10 - 9.33| = 0.67
|10 - 9.33| = 0.67
|11 - 9.33| = 1.67
|12 - 9.33| = 2.67
|12 - 9.33| = 2.67
|14 - 9.33| = 4.67
|15 - 9.33| = 5.67
|17 - 9.33| = 7.67
|18 - 9.33| = 8.67
|19 - 9.33| = 9.67

Step 3: Calculate the sum of the absolute deviations
Sum of absolute deviations = 8.33 + 5.33 + 3.33 + 2.33 + 0.67 + 0.67 + 0.67 + 1.67 + 2.67 + 2.67 + 4.67 + 5.67 + 7.67 + 8.67 + 9.67
Sum of absolute deviations = 63.35

Step 4: Find the Mean Absolute Deviation
MAD = Sum of absolute deviations / Number of data points
MAD = 63.35 / 15
MAD = 4.22 (rounded to two decimal places)

Therefore, the Mean Absolute Deviation (MAD) for the provided data set is 4.22.
Answered by GPT 3.5
To find the Interquartile Range (IQR) for the data set {1, 4, 6, 7, 9, 10, 10, 11, 12, 12, 14, 15, 17, 18, 19}, follow these steps:

Step 1: Arrange the data in ascending order:
1, 4, 6, 7, 9, 10, 10, 11, 12, 12, 14, 15, 17, 18, 19

Step 2: Find the first quartile (Q1) and the third quartile (Q3).

Q1: The median of the lower half of the data set:
Lower half: 1, 4, 6, 7, 9, 10
Median of lower half = (6 + 7) / 2 = 6.5

Q3: The median of the upper half of the data set:
Upper half: 12, 12, 14, 15, 17, 18, 19
Median of upper half = (14 + 15) / 2 = 14.5

Step 3: Calculate the IQR:
IQR = Q3 - Q1
IQR = 14.5 - 6.5
IQR = 8

Therefore, the Interquartile Range (IQR) for the data set {1, 4, 6, 7, 9, 10, 10, 11, 12, 12, 14, 15, 17, 18, 19} is 8.