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.\n\npossible sums\n|sum|frequency|\n|----|----|\n|5|1|\n|7|2|\n|9|3|\n|11|4|\n|13|3|\n|15|2|\n|17|1|\n\nwhat statement is true about the mean of the sums of the two spinners?\no the mean is 12.\no the mean is 16.\no the mean is the same as the median.\no the mean is the same as the range.

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.\n\npossible sums\n|sum|frequency|\n|----|----|\n|5|1|\n|7|2|\n|9|3|\n|11|4|\n|13|3|\n|15|2|\n|17|1|\n\nwhat statement is true about the mean of the sums of the two spinners?\no the mean is 12.\no the mean is 16.\no the mean is the same as the median.\no the mean is the same as the range.

Answer

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 $\bar{x}=\frac{176}{16}=11$

Step4: Find the median

Arrange the data in ascending - order of frequency. 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 5, 7, and 9. The 7th - 10th data points have a sum of 11. So the median is 11.

Step5: Calculate the range

The range is $17 - 5=12$

Answer:

The mean is the same as the median.