Question

using statistical measures to compare probabilities
the table compares the expected outcomes to the actual outcomes of the sums of 36 rolls of 2 standard number cubes.
sum expected actual
2 1 1
3 2 0
4 3 5
5 4 5
6 5 6
7 6 5
8 5 3
9 4 3
10 3 4
11 2 3
12 1 1
which comparisons are true of the frequency table? check all that apply.
both data sets are symmetrical.
the mean of the actual sums is more than the mean of the expected sums.
the range of the sums is the same for both sets of data.
the standard deviation of the actual sums is less than that of the expected sums.
the medians and quartiles are the same in both sets.

Explanation:

Step1: Calculate the range for expected and actual

Expected range: $12 - 2=10$. Actual range: $12 - 2 = 10$.

Step2: Analyze symmetry

The expected data has a symmetric distribution around 7. The actual data is not symmetric.

Step3: Consider means

We would need to calculate the means using $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}f_{i}}{\sum_{i = 1}^{n}f_{i}}$. Without calculation, we can see from the data that the actual values are not consistently larger than expected to conclude the mean of actual is more.

Step4: Consider standard - deviation

We would need to calculate using $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}f_{i}}{\sum_{i = 1}^{n}f_{i}}}$. Just from the data, we can't conclude the actual standard - deviation is less.

Step5: Consider medians and quartiles

We would need to order the data and find the median and quartiles. Without calculation, we can't conclude they are the same.

Answer:

The range of the sums is the same for both sets of data.