violet creates two spinners for a game. each spinner is spun once, and the sum is recorded. the table…

violet creates two spinners for a game. each spinner is spun once, and the sum is recorded. the table represents the sums of the spinners and the frequency of each sum. what statement is true about the mean of the sums of the two spinners? possible sums sum frequency 5 1 7 2 9 3 11 4 13 3 15 2 17 1 the mean is 12. the mean is 16. the mean is the same as the median. the mean is the same as the range.
Answer
Explanation:
Step1: Calculate the sum of products
First, find the product of each sum - frequency pair and then sum them up. [ (5\times1)+(7\times2)+(9\times3)+(11\times4)+(13\times3)+(15\times2)+(17\times1)=5 + 14+27 + 44+39+30+17=176]
Step2: Calculate the total frequency
Sum up all the frequencies. [1 + 2+3 + 4+3+2+1=16]
Step3: Calculate the mean
Divide the sum of products by the total frequency. [ \text{Mean}=\frac{176}{16}=11]
Step4: Find the median
Arrange the data in ascending - order of sums with their frequencies. There are 16 data points. The median is the average of the 8th and 9th ordered data - points. The first (1 + 2+3=6) data - points have sums less than 11, and the first (1 + 2+3 + 4 = 10) data - points have sums of 11 or less. So, the 8th and 9th data - points are 11, and the median is 11.
Step5: Find the range
The range is the difference between the maximum and minimum values. The maximum sum is 17 and the minimum sum is 5. So, the range is (17 - 5=12).
Answer:
The mean is the same as the median.