Question

find the mean, median, and mode of the set of values.

age (years)	frequency
12	9
13	11
14	13
15	8
16	7
17	2

find the mean. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
the mean is approximately \\(\square\\) years. (round to two decimal places as needed.)

Explanation:

Step1: Calculate total age

Multiply each age by its frequency and sum:
\(11\times5 + 12\times9 + 13\times11 + 14\times13 + 15\times8 + 16\times7 + 17\times2\)
\(= 55 + 108 + 143 + 182 + 120 + 112 + 34\)
\(= 55 + 108 = 163\); \(163 + 143 = 306\); \(306 + 182 = 488\); \(488 + 120 = 608\); \(608 + 112 = 720\); \(720 + 34 = 754\)

Step2: Calculate total frequency

Sum all frequencies:
\(5 + 9 + 11 + 13 + 8 + 7 + 2 = 55\)

Step3: Compute the mean

Mean = \(\frac{\text{Total Age}}{\text{Total Frequency}} = \frac{754}{55} \approx 13.71\)

Answer:

\(13.71\)