If Sonya were to make a dot plot of the combined data, explain the characteristics she should see. (Is there overlap in the data? Can she tell there are two sets being measured, or will it look like one set of data? Does the information shown in the dot plot indicate which data set has the most variability?)
If Sonya were to make a dot plot of the combined data, she should be able to see the individual data points represented by dots along a number line.
If there is overlap in the data, it will be reflected by the dots appearing on top of each other. This will indicate that there are values which are the same or very close to each other.
If there are two sets being measured, Sonya should be able to visually distinguish them on the dot plot. There will be distinct clusters or groups of dots corresponding to each set. This will help her identify the separate data sets.
The dot plot may provide some indication of which data set has the most variability. If there is a larger spread or dispersion of dots along the number line for one set of data compared to the other, it suggests that the data set with the larger spread has more variability. Sonya can observe the distance between the dots to determine the spread of the data.
If Sonya were to make a box-and-whisker plot of each data set, explain the characteristics she should see. (Is there overlap in the data? Is there overlap within the 1st and 3rd quartiles? Does the information shown in the box-and-whisker plots say anything about which data set has the most variability?)
If Sonya were to make a box-and-whisker plot of each data set, she should expect to see the following characteristics:
1. Overlap in the data: The box-and-whisker plots will have separate boxes for each data set, and there may be overlap between these boxes. The extent of overlap will indicate the degree to which the two sets share similar values. If the boxes overlap significantly, it suggests that there are similar values present in both data sets.
2. Overlap within the 1st and 3rd quartiles: The 1st quartile represents the lower 25% of the data, and the 3rd quartile represents the upper 25% of the data. Within the individual box in each plot, there may be some overlap between the values within the 1st and 3rd quartiles. This suggests that there are similar values between the lower and upper ends of each data set.
3. Variability: The box-and-whisker plot provides information about the variability in each data set. The length of the whiskers and the size of the box can give an indication of the data's spread. A longer whisker and a larger box suggest a greater spread and higher variability in the data set. Sonya can compare the lengths of the whiskers and boxes between the two plots to determine which data set has the most variability.