The image you've uploaded contains a statistical problem related to a dataset of shoe sizes for some students. There are several columns involving the frequency of each size and additional calculations, including mean, absolute deviation, squared deviation, and weighted values based on frequency.

Here's a breakdown of the table and tasks:

Table columns (unfinished):

1. x: Shoe size values.
2. f: Frequency of each shoe size.
3. Several other columns involving absolute and squared deviations from the mean.

The table is likely designed to calculate:

1. Mean (Meðaltal): The average shoe size.
2. Range (Dreifisvið): The difference between the largest and smallest sizes.
3. Mean Absolute Deviation (Meðalfrávik): Average of the absolute deviations from the mean.
4. Standard Deviation (Staðalfrávik): Measure of how spread out the values are from the mean.

Steps to help you solve the problem:

1. Fill in the missing values: Calculate the mean first, then use it to complete the remaining columns for the absolute and squared deviations.
2. Find the measures:
   • Mean: $\bar{x} = \frac{\sum(f \cdot x)}{n}$
   • Range: Maximum size - Minimum size.
   • Mean Absolute Deviation: $\frac{\sum(f \cdot |x - \bar{x}|)}{n}$
   • Standard Deviation: $\sqrt{\frac{\sum(f \cdot (x - \bar{x})^2)}{n}}$

Would you like to proceed with these calculations, or do you need any further clarification on how to fill out the table and complete the tasks?

Related Questions:

1. How is the mean used to complete the table's absolute deviation and squared deviation columns?
2. What is the significance of the frequency $f$ when calculating these statistical measures?
3. How does the range help describe the spread of the shoe sizes?
4. What is the relationship between mean absolute deviation and standard deviation?
5. How does increasing the sample size affect the reliability of these measures?

Tip:

When calculating variance or standard deviation, remember that you are measuring the spread around the mean, so outliers can significantly influence these values.