Based on the data showing the number of pieces of …

Mathematics Questions

Based on the data showing the number of pieces of mail delivered to a single home each day for three weeks, which two statements are true about a graph representing the data? 1. The number line of a dot plot would start at 1. 2. A dot plot would show 7 points for numbers greater than 2. 3. The intervals on a histogram should be 0 to 2, 3 to 4, and 5 to 6. 4. A histogram would have a maximum of 7 bars. 5. A histogram should not show a bar that includes 0 pieces of mail.

Short Answer

The analysis explains that a dot plot visually represents data points, showing 7 dots for values greater than 2, while a histogram showcases the frequency of these values with a maximum of 7 bars. These findings confirm that the dot plot displays 7 points and the histogram comprises 7 bars representing distinct values.

Step-by-Step Solution

Step 1: Understanding Dot Plots

A dot plot visually represents data points using dots, where each dot corresponds to a specific data value. For example, if you have data points greater than a certain number, each of those data points will be shown as a dot above that specific value on the number line. In the given scenario, there are 7 distinct data points greater than 2, leading to a dot plot that illustrates 7 dots positioned accordingly.

Step 2: Exploring Histograms

A histogram displays the frequency of data within specified ranges (or ‘bins’) using bars. Each bar’s height indicates how many data points fall within that range. In this case, with 7 different values ranging from 0 to 6, the histogram will consist of 7 bars representing these distinct values, showcasing their frequency in the dataset.

Step 3: Confirming the True Statements

From the explanations above, we can summarize the findings concerning the dot plot and histogram. The two true statements confirmed by the analysis are:

  • B. The dot plot would show 7 points for numbers greater than 2.
  • D. The histogram would have a maximum of 7 bars for the different data values.

Related Concepts

Dot Plot

A graphical representation of data points using dots where each dot corresponds to a specific data value, showing the frequency of occurrences along a number line.

Histogram

A bar chart that represents the frequency distribution of data within specified ranges, where the height of each bar reflects the number of data points within a certain interval or ‘bin’.

Data Frequency

The number of times a particular value or range of values appears in a dataset, often represented visually in tools like dot plots and histograms.

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