Question

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.

Explanation:

Step1: Calculate the sum of the products of sums and frequencies

\[ (5\times1)+(7\times2)+(9\times3)+(11\times4)+(13\times3)+(15\times2)+(17\times1)=5 + 14+27 + 44+39+30+17=176\]

Step2: Calculate the total frequency

\[1 + 2+3 + 4+3+2+1=16\]

Step3: Calculate the mean

The mean $\bar{x}=\frac{176}{16}=11$.
Now, find the median. There are $n = 16$ data - points. The median is the average of the 8th and 9th ordered data - points.
The cumulative frequencies are: 1 (for sum = 5), 1+2 = 3 (for sum = 7), 3 + 3=6 (for sum = 9), 6+4 = 10 (for sum = 11). So, the 8th and 9th ordered data - points are both 11, and the median is 11.
The range is $17 - 5=12$.

Answer:

The mean is the same as the median.