Emily measured the depth of water in a bathtub at two minute intervals after the tap was turned off and the stopper released. The table shows her data.
a) Make a scatter plot for the data.
b) Describe the correlation of the scatter plot.
c) What will the approximate depth be at 15 seconds?
Time-(in minutes) | Depth-(in cm)
2 | 4
4 | 41
6 | 38
8 | 37
10 | 32
12 | 24
14 | 20
16 | 19
18 | 13
a) To make a scatter plot for the data, we will plot the time (in minutes) on the x-axis and the depth (in cm) on the y-axis.
Time (in minutes) Depth (in cm)
----------------- -----------------
2 4
4 41
6 38
8 37
10 32
12 24
14 20
16 19
18 13
b) Looking at the scatter plot, we can determine the correlation. A correlation describes the relationship between two variables. In this case, we are looking for the relationship between time and depth.
From the scatter plot, it appears that the depth of water decreases as time increases. The points on the graph are not perfectly aligned along a straight line, but it can be observed that there is a general downward trend. Therefore, the correlation in this scatter plot is negative.
c) To estimate the approximate depth at 15 seconds, we need to determine where 15 seconds falls on the time axis.
There are 60 seconds in a minute, so 15 seconds is equal to 15/60 = 1/4 of a minute.
Looking at the time axis, the closest values are 12 minutes (720 seconds) and 14 minutes (840 seconds). Since 15 seconds is closer to 14 minutes, we can estimate that the approximate depth at 15 seconds would be closest to the depth at 14 minutes, which is 20 cm.
a) To make a scatter plot for the data, you can use a graphing tool, such as a spreadsheet program or online graphing tool.
First, create a coordinate grid on a piece of graph paper or in your graphing tool. Label the x-axis as "Time (in minutes)" and the y-axis as "Depth (in cm)."
Next, plot each data point on the graph. For example, for the first data point (2, 4), locate the point on the x-axis at 2 and on the y-axis at 4. Repeat this process for all the data points. Connect the points with a smooth curve or line.
b) To describe the correlation of the scatter plot, you would need to analyze the overall trend of the data points. There are a few possibilities for correlation:
- Positive correlation: If the data points generally form an upward trend, it indicates a positive correlation. This means that as the time increases, the depth of the water also increases.
- Negative correlation: If the data points generally form a downward trend, it indicates a negative correlation. This means that as the time increases, the depth of the water decreases.
- No correlation: If the data points do not form any apparent trend, it indicates no correlation. This means that there is no consistent relationship between time and depth.
Based on the given data points, it appears that the scatter plot would show a negative correlation. As time increases, the depth of the water decreases.
c) To approximate the depth at 15 seconds, we need to convert the time from seconds to minutes. Since there are 60 seconds in a minute, 15 seconds is equal to 15/60 = 0.25 minutes.
Using the scatter plot or the equation that best fits the data (if available), find the corresponding depth value for a time of 0.25 minutes. In this case, because we don't have an equation or a finely grained scatter plot, we can make an estimate based on the given data points.
From the data, the closest time values we have are 12 minutes and 14 minutes. The corresponding depths are 24 cm and 20 cm, respectively. Since 15 seconds is closer to 14 minutes (840 seconds), we can assume the depth will be closer to 20 cm.
Therefore, the approximate depth at 15 seconds will be around 20 cm.
You can find handy least-squares and correlation coefficient calculators at
www.mathsisfun.com/data/least-squares-calculator.html
www.mathsisfun.com/data/correlation-calculator.html