Note: Your teacher will grade your responses to questions 18 and 19 to ensure that you receive proper credit for your answers.
You are surveying students to find out their opinion of the quality of food served in the school cafeteria. You decide to poll only those students who buy hot lunch on a particular day. Is your sample random? Explain.
3 answers
No, the sample is not random. A random sample would involve selecting students from the entire population of the school, regardless of whether they buy hot lunch or not. By only poll students who buy hot lunch on a particular day, the sample is biased, as it excludes those who bring their own lunch or do not eat at the cafeteria on that particular day. Therefore, the results cannot be generalized to the entire population of the school.
The table shows the rainfall, in inches, in the month of July for the years 2006 through 2011.
Year
2006
2007
2008
2009
2010
2011
Rainfall
4.5
4.4
4.1
4.2
3.9
4.0
Alex used the data to make the graph below.
A line graph representing the data in the table is shown.A line graph is titled July Rainfall.
The horizontal axis is labeled Year and is equally spaced. The axis scale starts at 2006 increases by 1 until ending at 2011.
The vertical axis is labeled Rainfall in inches and is equally spaced. The axis scale starts at 3.6 and increases by 0.1 until ending at 4.6.
The data points represented in the tabled are connected by line segments from left to right.
a) In what way could the graph be misleading?
b) How could you redraw the graph so that it is less misleading?
Year
2006
2007
2008
2009
2010
2011
Rainfall
4.5
4.4
4.1
4.2
3.9
4.0
Alex used the data to make the graph below.
A line graph representing the data in the table is shown.A line graph is titled July Rainfall.
The horizontal axis is labeled Year and is equally spaced. The axis scale starts at 2006 increases by 1 until ending at 2011.
The vertical axis is labeled Rainfall in inches and is equally spaced. The axis scale starts at 3.6 and increases by 0.1 until ending at 4.6.
The data points represented in the tabled are connected by line segments from left to right.
a) In what way could the graph be misleading?
b) How could you redraw the graph so that it is less misleading?
a) The graph could be misleading because the difference in rainfall from year to year is very small, and the vertical axis scale is compressed. This makes it appear as though there is a larger difference in rainfall than there actually is, leading to potentially incorrect interpretations or conclusions.
b) To make the graph less misleading, the vertical axis scale could be expanded to better represent the small differences in rainfall from year to year. For example, the scale could start at 3.8 and increase by 0.1 until ending at 4.6. This would make the differences in rainfall between years appear more accurate and less exaggerated. Another option could be to use a bar graph instead of a line graph, as it would make it easier to see the differences in rainfall between years more clearly.
b) To make the graph less misleading, the vertical axis scale could be expanded to better represent the small differences in rainfall from year to year. For example, the scale could start at 3.8 and increase by 0.1 until ending at 4.6. This would make the differences in rainfall between years appear more accurate and less exaggerated. Another option could be to use a bar graph instead of a line graph, as it would make it easier to see the differences in rainfall between years more clearly.
7 answers