Mathematical Reflection 1 Data Distribution p. 27 1)Use the situation below to help you answer parts (a)-(e) Students collected data from their classmates to answer each of these three questions: What is the typical bedtime for students? What are students’ favorite kinds of pets? What is the typical number of pets students have?

a. What measures are used to describe variability? Frequencies (counts or percents) are one measure that describe variability. The range also is used with numerical data to describe variability. The variability is closely clustered here because the range is only 1.5 cm.

b. Define the range of distribution of data so a sixth-grader would understand. The range describes the differences between the maximum and minimum values in a distribution of numerical data. It is a measure of variability and provides some information about the variability in a data set. Max: 56.5 Min:

c. How would you help a sixth-grade student understand the difference between categorical data and numerical data? Categorical data are grouped by category like: Months of year Kinds of pets Numerical data is data consisting of numbers, not categories, such as: Heights of students Length of table

d. What does it mean when we say categorical data vary? Categorical data varies when there are a variety of different categories. For example: Favorite kinds of pets Dog Bird Cat Hamster Rabbit Frog e. What does it mean when we say Numerical data vary? Numerical data varies when the values of the data are not the same; they may be spread out. For example: Number of people living in you home One Two Three Four Five Six

2. In which situations might you report frequencies of data using actual counts? In which might you use percents? How do you decide? Actual counts can be used to report frequencies when the numbers of data values in the sets are the same. For example: Number of pets students have One Two Three Percents can be used to report frequencies when the numbers in the data sets are different. The percent frequency will show how much your data count represents out of the total. For example: Number of M & M’s in a bag Green - 18 % Brown – 33% Red – 7%

3. Describe how displaying data in tables or graphs can help you identify patterns or determine what is typical about a distribution. In a table or graph you can see a change in the count or percent over time. You can also find out what is typical by finding the mean or the median of the data set.