The content of this uploaded file seems to be the same as the earlier one, asking to find the mean, median, mode, and population standard deviation for the provided dataset.

Let me recap the calculations with clear steps once again.

Dataset:

$19, 23, 25, 28, 30, 32, 33, 33$

1. Mean:

$\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$ $\text{Sum} = 19 + 23 + 25 + 28 + 30 + 32 + 33 + 33 = 243$ $\text{Mean} = \frac{243}{8} = 30.4$

2. Median:

The median is the middle value(s) when the dataset is ordered. Since $N = 8$ (even), the median is the average of the 4th and 5th values: $\text{Median} = \frac{\text{4th value + 5th value}}{2}$ $\text{Median} = \frac{28 + 30}{2} = 29.0$

3. Mode:

The mode is the value(s) that occurs most frequently:

• $33$ appears twice, while all other values appear once. $\text{Mode} = 33$

4. Population Standard Deviation:

The formula for population standard deviation is: $\sigma = \sqrt{\frac{\sum{(x_i - \mu)^2}}{N}}$ Where:

• $x_i$ = each data value,
• $\mu$ = mean,
• $N = 8$.

Step 1: Deviations from the mean ($x_i - \mu$): $\mu = 30.4$