A survey is conducted and the number of people in each household and the amount spent on groceries each week is collected from each respondent. What type of graph would be appropriate to display this data? Explain your choice.
Histogram
Bar graph
Scatter plot
Dot plot
A histogram would be the most appropriate type of graph to display this data.
A histogram is a type of graph that shows the distribution of a continuous dataset. In this case, the number of people in each household and the amount spent on groceries each week are continuous variables. The histogram will allow us to visualize the frequency or count of households for each range of number of people and amount spent on groceries, respectively.
A bar graph is a type of graph that shows the distribution of categorical variables, not continuous variables. A scatter plot is used to display the relationship between two continuous variables, which is not the case here. A dot plot, while it can display continuous variables, is better suited for smaller data sets as it can become overcrowded with larger datasets.
To determine the appropriate type of graph to display this data, it is important to consider the variable types and the relationships between them.
In this case, we have two variables: the number of people in each household (which can be considered discrete) and the amount spent on groceries each week (which can be considered continuous).
A histogram would be an appropriate choice for this data. Histograms are used to display the distribution of continuous data by dividing it into intervals or bins and showing the frequency or count of observations falling into each bin. In this case, the number of people can be grouped into intervals (e.g., households with 1-2 people, 3-4 people, 5-6 people, etc.), and the amount spent on groceries can be grouped into corresponding intervals (e.g., $0-$50, $51-$100, $101-$150, etc.).
Using a histogram allows us to understand the distribution of household sizes and the corresponding amount spent on groceries. It shows the frequency or count of observations within each interval, providing a visual representation of how the variables are related.
Other graph types may not be as suitable:
- A bar graph is typically used to compare discrete categorical data, such as different household sizes and their spending categories. However, it may not effectively capture the continuous relationship between the variables.
- A scatter plot is used to display the relationship between two continuous variables. While it could be used if we want to analyze the relationship between household size and grocery spending for each individual respondent, it may not provide a clear overall picture of the data distribution.
- A dot plot is similar to a scatter plot, but it shows individual data points instead of plotting pairs of variables. While it can display the individual responses, it may not be as efficient in representing the distribution of the overall data.
Thus, a histogram would be the most appropriate graph choice to display the given data.