Ms. Monroe mixes 200 cubes of 4 different colors for a project. She then uses a scoop to place 20 cubes into each of 10 paper bags. Each group records the number of cubes of each color in a bag. The number of red cubes for the 10 groups are recorded in the graph.
Accepted Solution
A:
Answer:The mean no. of red cubes is more than the median no. of red cubes.Step-by-step explanation:According to the question, we can prepare the following table denoting the no. of bags containing any number of red cube(s). The no. of red cubes in each bag can theoretically be any no. between 0 and 20 (both end inclusive) as in total each bag contains 20 cubes of different colors.There are as a whole 10 bags (given).No. of red cubes No. of bags [tex](x_{i}f_{i})[/tex] [tex](x_{i})[/tex] [tex](f_{i})[/tex] 0 2 0 1 0 0 2 2 4 3 1 3 4 1 4 5 0 0 6 1 6 7 2 14 8 1 8 9 0 0 10 0 0 Total 10 39Now, no. of bags containing no. of red cubes above 10 is 0 [since there are as a whole 10 bags only] So, from the table we get that mean no, of red cubes in each bag = [tex]\frac {\sum_{i =1}^{10}x_{i}f_{i}}{\sum_{i=1}^{10}f_{i}}[/tex] = 39/10 = 3.9Also, from the table, we get that, no. of bags with no. of red cubes ≤ 3= (2 + 2 + 1) = 5and, no. of bags with no. of red cubes ≥ 4 = (1 + 1 + 2 + 1) = 5Also there are 1 bag each for no. of red cubes = 3 and 4So. median no. of red cubes = (3 + 4)/2 = 3.5So, we get that the mean no. of red cubes is more than the median no. of red cubes.