Edmentum Integrated Math1 Unit10 Activity: Inferences and Conclusions from Data

Social Science Statistics Line of Best Fit:

How do the columns titled Number and % of Total Population relate to the columns titled Total?

Generate a histogram of the state data in the column titled % of Total Population using the Histogram Applet and paste or attach an image of the histogram in the box below. Note that you can copy a column of data from the spreadsheet and paste it into the Data box in the Applet. Set the x-axis limits and the interval size so that you get the best picture of the data and label the x-axis.

Generate a box plot of the state data in the column titled % of Total Population using the Box Plot Applet and paste or attach an image of the box plot in the box below. Note that you can copy a column of data from the spreadsheet and paste it into the Data box in the Applet. Label the x-axis.

Describe the shape, spread, and skew (if any) of the data.

Examine the graphs and the information provided by the two Applets. Record the mean and the median of the data set.

Return to the Box Plot Applet, Exclude Outliers, and then click Update. Notice that the plot boundaries contract, with outliers showing as small circles outside of the whiskers of the plot. Based on this plot, how many outliers are there?

Which states are represented by the outlier data? What do these states have in common that might contribute to making them outliers?

If you were in the diamond business, or if you are looking to purchase a diamond, you need to know how to price diamonds accurately. Otherwise, you would be losing money by selling too low or losing customers by selling to high. Having some sort of “price ruler” can be very useful. In this task, you will examine data for the most extravagant diamonds on the market and begin building a price ruler.

Generate a scatter plot of the weight versus price of these diamonds using the Scatter Plot Applet and paste or attach an image of the scatter plot in the box below. Note that you can copy a column of data from the spreadsheet and paste it into the Data box in the Applet. Label the x- and y-axes.

Describe the relationship between the price and the weight.

Return to the Scatter Plot Applet, click the Line of Best Fit box, and then click Update. Notice that this graphs a linear regression that approximates the relationship between the price and the weight of the diamonds. Record the equation of the regression line and the value of the correlation coefficient. Is this line a good fit for predicting the price of a diamond?

Using the equation for the best-fit line, estimate the price of diamonds weighing more than 3.5 carats and enter the values in the table. Compare these estimates to the actual sales prices for these three diamonds. Do the estimates match the actual sales prices?

The regression equation you obtained in Part 10 is linear. However, the actual data values do not seem to fit a linear shape - there is an upward curve. Another option is to use a different shape of regression equation that might better fit the data. Return to the Scatter Plot Applet, click the Custom Fit box, and then click Update. Notice that this graphs a quadratic curve, shown in green, that seems to be a better approximation of the data. Record the value of the correlation coefficient. Is a quadratic curve a better fit for predicting the price of a diamond?

Using the equation for the quadratic curve, estimate the price of diamonds weighing more than 3.5 carats and enter the values in the table. Compare these estimates to the prices obtained in Part 11 and the actual sales prices for these three diamonds. Which curve produces the better estimate of the actual sales prices?