Answer/Explanation:
Given==>
number of data set = 11 (i.e. 11 people with name lengths collected)
Median name length = 6 (one of the 11 people has a name length of 6, and it is the middle value in the data set)
Required==>
a. Possible dot plot displaying the data where there is little variation (data varies a little)
b. Possible dot plot displaying the data where there is much variation (data varies a lot)
First, let's come up with possible data sets for each scenario bearing in mind what we're given and what we're required of:
a. Data set for name length for the first dot plot in which data varies little = 4, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8
Note: 6 is the median name length here. We also ensured the range of values for the data set which we want to use for the first dot plot is not much (i.e. range = 8 - 4 = 4).
b. Data set for name length for the second dot plot where there is much variation in the data set = 4, 5, 5, 5, 6, 6, 7, 9, 10, 10, 11
Note: 6 is also the median name length. Also, we ensured the range of the data set is much compared to the first data set we wrote out, so as to make the data show much variation. (I.e. range = 11 - 4)
Next is to to choose a scale for the dot plot we want to make, then use a dot to represent each values in the data set we have made up.
See attached picture below for the 2 possible dot plots (a & b) we have make to display the data.
