Compute the missing values in the table below. Round all values to 3 decimal places.
| data | mean | IQR | MAD | variance | standard deviation |
|---|---|---|---|---|---|
| {1, 2, 3} | 2 | 2 | 0.667 | 0.667 | 0.817 |
| {4, 5, 6} | 5 | 2 | 0.667 | 0.667 | 0.817 |
| {2, 4, 6} | 4 | 4 | 1.333 | 2.667 | 1.633 |
| {0, 5, 10} | 5 | 10 | 3.333 | 16.667 | 4.083 |
Formulas for measures of variability:
(recall: \( d_i = \) each data point, \(n = \) number of data, \( \mu = \) mean)
1. Which data set is most spread out? How can you tell?
The last data set is more spread out, which is evident because each measure of variability (IQR, MAD, variance, standard deviation) is higher for this data set. Also, the third data set is more spread out than the first two for similar reasons.
2. The second data set is +3 of the first data set. What measures changed and why?
The mean increased because each data point increased. The measures of variability (IQR, MAD, variance, standard deviation) did not change because the data are spread out the same.
3. The third data set is twice (×2) the first data set. What measures changed and why?
The mean increased because each data point increased. The measures of variability (IQR, MAD, variance, standard deviation) also increased because the data are now more spread out.