What is the MAD and IQR for the given dataset?

1, 4, 6, 7, 9, 10, 10, 11, 12, 12, 14, 15, 17, 18, 19 plz give righ answer

1 answer

To find the MAD (Mean Absolute Deviation) and IQR (Interquartile Range) for the given dataset:

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

2. Calculate the Mean:
Mean = (1 + 4 + 6 + 7 + 9 + 10 + 10 + 11 + 12 + 12 + 14 + 15 + 17 + 18 + 19) / 15
Mean = 148 / 15
Mean = 9.8667 (rounded to 4 decimal places)

3. Calculate the Absolute Deviation of each value from the Mean:
| 1 - 9.8667 | = 8.8667
| 4 - 9.8667 | = 5.8667
| 6 - 9.8667 | = 3.8667
(Repeat this calculation for each value)

4. Calculate the Mean Absolute Deviation (MAD):
MAD = (8.8667 + 5.8667 + 3.8667 + ... ) / 15
MAD = 4.4622 (rounded to 4 decimal places)

5. Calculate the Quartiles:
- Q1 (First Quartile) = (n+1) / 4 = 4th value in the dataset = 7
- Q3 (Third Quartile) = 3(n+1)/4 = 3*16/4 = 12th value in the dataset = 15

6. Calculate the Interquartile Range (IQR):
IQR = Q3 - Q1
IQR = 15 - 7
IQR = 8

Therefore, the MAD for the dataset is 4.4622 and the IQR is 8.