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Question

Part 1
Find the​ mean, median, and mode of the set of values.
Age​ (years)
10
11
12
13
14
15
16
Frequency
6
12
17
15
7
5
5
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Part 1
Find the mean. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
The mean is approximately
  
enter your response here years. ​(Round to two decimal places as​ needed.)
Part 2
Find the median. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
The median is
  
enter your response here years.
Part 3
Find the mode. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The mode is
  
enter your response here years. ​(Use a comma to separate answers as​ needed.)
B.
There is no mode.

Answer 1

Part 1:
Mean = Σ(f×x) / Σf
= (6×10 + 12×11 + 17×12 + 15×13 + 7×14 + 5×15 + 5×16) / (6 + 12 + 17 + 15 + 7 + 5 + 5)
= (60 + 132 + 204 + 195 + 98 + 75 + 80) / 67
= 844 / 67
= 12.59

Therefore, the mean is approximately 12.59 years.

Part 2:
To find the median, we need to arrange the data in ascending order.
10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16

Since there are 67 numbers, the median will be the average of the 34th and 35th term.
Median = (12 + 12) / 2
= 12

Therefore, the median is 12 years.

Part 3:
The mode is the number that appears most frequently.
The mode is 12 years.

Therefore, the correct choice is:
A. The mode is 12 years.