Question

tasneem has a sample of 12 bags of candy. she recorded the mass, in grams, of each bag. her data is shown. 46.6, 46.7, 46.7, 46.8, 46.8, 47.1, 47.2, 47.3, 47.5, 47.9, 48, 48.1
aalia has a different sample of 12 bags of candy. she recorded the mass, in grams, of each bag. the median mass for aalias sample is greater than the median mass of tasneems sample.
which dot - plot could represent aalias data?

Explanation:

Step1: Find Tasneem's median

Since there are $n = 12$ data - points (an even number of data - points), the median is the average of the $\frac{n}{2}=6$th and $(\frac{n}{2}+1) = 7$th ordered data - points. The ordered data for Tasneem is: 46.6, 46.7, 46.7, 46.8, 46.8, 47.1, 47.2, 47.3, 47.5, 47.9, 48, 48.1. The 6th value is 47.1 and the 7th value is 47.2. So, the median of Tasneem's data is $\frac{47.1 + 47.2}{2}=47.15$.

Step2: Analyze dot - plots for Aalia's data

For a set of 12 data - points (even number of data - points), the median is the average of the 6th and 7th ordered data - points.

• Option A: Looking at the dot - plot, if we order the data, the 6th and 7th values seem to be around 47 or less, so the median is less than 47.15.
• Option B: If we order the data from the dot - plot, the 6th and 7th values seem to be around 47 or less, so the median is less than 47.15.
• Option C: If we order the data from the dot - plot, the 6th and 7th values are such that the median is greater than 47.15.
• Option D: If we order the data from the dot - plot, the 6th and 7th values seem to be around 47 or less, so the median is less than 47.15.

Answer:

C