Here are dot plots that show the ages of people at two different parties. The mean of each distribution is marked with a triangle.

<p>A dot plot from 5 to 45 by 5’s. Age in years, labeled data set A. There is a red triangle indicated at 15, and the data set are as follows: 8 years, 12 dots. 10 years, 3 dots. 12 years, 1 dot. 15 years, red triangle. 36 years, 1 dot. 42 years, 1 dot. 44 years, 2 dots.</p>  

<p>A dot plot from 5 to 45 by 5’s. Age in years, labeled data set B. The data are as follows: 7 years, 1 dot. 8 years, 1 dot. 9 years, 1 dot. 10 years, 2 dots. 15 years, 1 dot. 16 years, 1 dot. 20 years, 2 dots and 1 red triangle. 22 years, 1 dot. 23 years, 1 dot. 24 years, 1 dot. 28 years, 1 dot. 30 years, 1 dot. 33 years, 1 dot. 35 years, 1 dot. 38 years, 1 dot. 42 years, 1 dot.</p>

What do you notice and what do you wonder about the distributions in the two dot plots?

Here are the ages of the people at one party, listed from least to greatest.

• 7
• 8
• 9
• 10
• 10
• 11
• 12
• 15
• 16
• 20
• 20
• 22
• 23
• 24
• 28
• 30
• 33
• 35
• 38
• 42

1. Split the data into 4 equal parts using 3 values called quartiles.
   1. Find the median of the data set and label it Q2 for second quartile. This splits the data into an upper half and a lower half.
   2. Find the middle value of the lower half of the data, without including the median. Label this value Q1 for first quartile
   3. Find the middle value of the upper half of the data, without including the median. Label this value Q3 for third quartile.

2. Label the least value in the set “minimum” and the greatest value “maximum.”

3. The values you have identified make up the five-number summary for the data set. Record them here.

   minimum: _____     Q1: _____     Q2: _____     Q3: _____     maximum: _____

4. The median of this data set is 20. This tells us that half of the people at the party were 20 years old or younger, and the other half were 20 or older. What do each of these other values tell us about the ages of the people at the party?

   1. The third quartile
   2. The minimum
   3. The maximum

1. Here is a dot plot that shows the lengths of Elena’s bus rides to school, over 12 days.

   

   Write the five-number summary for this data set. Show your reasoning.

2. The range is one way to describe the spread of values in a data set. It is the difference between the maximum and minimum. What is the range of Elena’s travel times?

3. Another way to describe the spread of values in a data set is the interquartile range (IQR). It is the difference between the third quartile (Q3) and the first quartile (Q1).

   1. What is the interquartile range (IQR) of Elena’s travel times?

   2. What fraction of the data values are between Q1 and Q3?

4. Here are 2 more dot plots.

   

   <p>A dot plot from 14 to 28 by 2's, labeled data set A. The dot plot begins at 14, number of dots above each increment of 1 is 0, 1, 3, 3, 1, 0, 0, 3, 1, 2, 3, 4, 1, 3, 1. </p>  

   

   <p>A dot plot from 14 to 28 by 2's, labeled data set B. The dot plot begins at 14, number of dots above each increment of 1 is 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 8, 2, 6, 3.</p>

   Without doing any calculations, predict:

   1. Which data set has the smaller range?

   2. Which data set has the smaller IQR?

5. Check your predictions by calculating the range and IQR for the data in each dot plot.