The image contains a problem in Danish related to statistics and data analysis. Let's break down the problem step-by-step:

Problem Analysis

a) Bestem kvartilsættet for fordelingen af pigernes højde.

This translates to: "Determine the quartile set for the distribution of the girls' heights."

The given data for the girls' heights in centimeters is: $155, 158, 158, 162, 165, 164, 169, 169, 169, 170, 172, 174, 174, 175, 183.$

b) Hvor mange af pigerne i A-klassen er højere end de 25% mindste af drengene på hf-kurset?

This translates to: "How many of the girls in A-class are taller than the shortest 25% of the boys in the hf-course?"

There is a boxplot shown for the heights of the boys, ranging from 155 cm to around 205 cm, with the first quartile (Q1) at approximately 175 cm.

Solution Steps

Part (a): Determining the Quartiles for the Girls' Heights

To find the quartile set (Q1, Q2, Q3) of the girls' heights:

1. Order the data: It is already ordered in ascending order.
2. Find the median (Q2): This is the middle value.
3. Find the first quartile (Q1): This is the median of the lower half.
4. Find the third quartile (Q3): This is the median of the upper half.

Part (b): Girls Taller than the 25% Shortest Boys

To solve this:

1. Identify the height corresponding to the first quartile (Q1) of the boys from the boxplot, which is around 175 cm.
2. Count the number of girls taller than this value.

Calculations

Let's compute these values.### Solutions

a) Quartiles for the Girls' Heights:

• First Quartile (Q1): 163 cm
• Second Quartile (Q2 or Median): 169 cm
• Third Quartile (Q3): 173 cm

b) Number of Girls Taller than the Shortest 25% of Boys:

• The height corresponding to the first quartile (Q1) of the boys is approximately 175 cm.
• Number of girls taller than 175 cm: 1 girl.

Would you like more details, or do you have any questions?

Related Questions

1. How would you calculate the interquartile range (IQR) for the girls' heights?
2. What does the boxplot tell us about the distribution of the boys' heights?
3. How would you determine the range of the girls' heights?
4. If the mean height of the girls is needed, how would you compute it?
5. What percentage of girls are below the median height?

Tip

Remember that quartiles divide a data set into four equal parts, with Q1, Q2, and Q3 representing the 25th, 50th, and 75th percentiles, respectively.