Question

1. wade and riley ride their bikes to school each morning. they want to compare... the longest time to ride their bike to school throughout the week.

a. is the data numerical or categorical?
b. what type of data display would be appropriate to display the data?

1. jayna keeps track of the daily low temperatures for november. she wants to find the average low temperature for the month of november.

a. what type of data display should jayna use to display the data?
b. make a data display.
chart: daily low temperatures (°f) for november

1. communicate and justify amy wants to keep a record of how she spends money each month. she decides to display her data in a circle graph. do you agree a circle graph is an appropriate graph for this data set? why or why not?

chart: category, percentage of money

1. higher order thinking why are certain data displays only able to be used for numerical data and not categorical data?
2. melanie collects data about the number of text messages students send each day.

chart: number of text message, data values
select all the true statements
☐ the data set is numerical data.
☐ the data set is categorical data.
☐ the data set has an outlier.
☐ the data set does not have an outlier.
☐ a circle graph is an appropriate data display for this data.
☐ a box plot is an appropriate data display for this data.
84 7-7 choose the best representation (box plots)

Explanation:

Question 12: Analyzing the Data Set of Text Messages

Step 1: Identify Data Type

The data consists of the number of text messages (numerical values: 94, 105, 87, 76, 110, 80, 101, 113, 85). Numerical data represents quantities, so this is numerical data.

Step 2: Check for Outliers

First, order the data: \( 76, 80, 85, 87, 94, 101, 105, 110, 113 \).

• Find the median (middle value): \( 94 \).
• Lower quartile (\( Q_1 \)): Median of the lower half (\( 76, 80, 85, 87 \)) is \( \frac{80 + 85}{2} = 82.5 \).
• Upper quartile (\( Q_3 \)): Median of the upper half (\( 101, 105, 110, 113 \)) is \( \frac{105 + 110}{2} = 107.5 \).
• Interquartile range (IQR): \( Q_3 - Q_1 = 107.5 - 82.5 = 25 \).
• Lower bound: \( Q_1 - 1.5 \times \text{IQR} = 82.5 - 37.5 = 45 \).
• Upper bound: \( Q_3 + 1.5 \times \text{IQR} = 107.5 + 37.5 = 145 \).

All data points (76–113) lie within 45–145, so no outliers.

Step 3: Evaluate Data Displays

• Circle graph: Used for showing parts of a whole (percentages/proportions). This data is individual values, not parts of a whole, so inappropriate.
• Box plot: Used for numerical data to show spread, median, quartiles, and outliers. Appropriate for this numerical data.

True Statements:

• The data set is numerical data. (True, as it’s quantities of text messages.)
• The data set does not have an outlier. (True, as all values lie within bounds.)
• A box plot is an appropriate data display for this data. (True, box plots work for numerical data.)

Answer:

• The data set is numerical data.
• The data set does not have an outlier.
• A box plot is an appropriate data display for this data.

(Select the checkboxes for these three statements.)