Let's go through the problem in the image. It describes a statistical study by Sara where she asked her classmates (29 students, excluding herself) about the number of SMS messages they sent during the past week. The results are shown in a boxplot, and you're tasked with answering various questions based on this data.

Question Breakdown:

a) Kvartilsavståndet (Interquartile range): The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). In the boxplot:

• The first quartile (Q1) is at 6.
• The third quartile (Q3) is at 22.

So, to find the interquartile range: $\text{IQR} = Q3 - Q1 = 22 - 6 = 16.$

b) Variationsbredden (Range): The range is the difference between the maximum and minimum values shown in the data. From the boxplot:

• The minimum value is 6.
• The maximum value is 65.

So, the range is: $\text{Range} = 65 - 6 = 59.$

c) Sara's SMS count and median: If Sara had sent 52 SMS messages, we need to check how the median would change if we include this value.

The median is the middle value in an ordered data set. Since there are 29 students, with Sara’s data included, there would be 30 data points. This means the median would be the average of the 15th and 16th values in the sorted list. Given that the current median (from the boxplot) appears to be around 13, adding Sara's data (52) should not affect the overall median, because 52 is much higher than the existing data.

d) Classmates with more than 22 SMS: Two classmates have sent exactly 22 SMS. To find how many classmates sent more than 22 SMS, we count the number of data points greater than 22 in the boxplot. From the boxplot, we see that values greater than 22 are in the far right tail. Thus, to determine how many classmates sent more than 22 SMS, count the number of values beyond the 22 mark.

Would you like a more detailed explanation for any of these parts or further analysis of other questions from the image?