The image presents a statistical problem where a survey is conducted among 21 families, asking how many times they've lost a remote during April. The following parts need to be solved:

Given Data:

The data set is:
2, 14, 21, 5, 1, 0, 1, 2, 14, 7, 0, 4, 3, 0, 10, 5, 9, 10, 5, 4, 5

The tasks involve:

a) Calculate:

• Mean (Medelvärde): Formula $\bar{x} = \frac{\sum x_i}{n}$
• Median: The middle value when data is arranged in ascending order.
• Mode (Typvärde): The most frequently occurring value.

b) Find:

• Range (VB): The difference between the largest and smallest values.
• Interquartile Range (IQR): The difference between the 75th percentile (Q3) and 25th percentile (Q1).

c) Calculate:

• Variance $s^2$: Using the formula $s^2 = \frac{1}{n} \left( \sum x_i^2 - \frac{\left( \sum x_i \right)^2}{n} \right)$ Given: $\sum x_i = 135, \quad \sum x_i^2 = 1473$
  • Standard Deviation: $s = \sqrt{s^2}$

Let me now work through the required steps to solve this.Here are the results for the statistical analysis of the given dataHere are the results for the statistical analysis of the given

a) Mean, Median, and Mode:

• Mean (Medelvärde): $\bar{x} = 5.81$
• Median: 5.0
• Mode (Typvärde): 5 (the most frequently occurring value)

b) Range and IQR:

• Range (VB): 21 (difference between the maximum 21 and minimum 0)
• Interquartile Range (IQR): 7.0

c) Variance and Standard Deviation:

• Variance $s^2$: 28.82
• Standard Deviation $s$: 5.37

Let me know if you'd like more details on any of these calculations!

5 Related Questions:

1. What is the difference between population and sample variance?
2. How is the IQR useful in detecting outliers?
3. Can a data set have more than one mode?
4. Why is the standard deviation preferred over variance in some cases?
5. How would the results change if the data set size was larger?

Tip: Always ensure data is arranged in ascending order when finding the median or quartiles.