Question

find the mean, median, and mode of the set of values
age (years) | frequency
11 | 5
14 | 9
12 | 14
16 | 17
17 | 5
18 | 4
19 | 3

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.)

find the median. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
the median is \\(\square\\) years.

find the mode. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the mode is \\(\square\\) years. (use a comma to separate answers as needed.)
b. there is no mode.

Explanation:

Step1: Calculate total frequency

First, sum all frequencies to find the total number of data points.
$\sum f = 5 + 5 + 14 + 17 + 9 + 4 + 3 = 57$

Step2: Calculate weighted sum for mean

Multiply each age by its frequency, then sum these products.
$\sum (x \cdot f) = (13 \times 5) + (14 \times 5) + (15 \times 14) + (16 \times 17) + (17 \times 9) + (18 \times 4) + (19 \times 3)$
$\sum (x \cdot f) = 65 + 70 + 210 + 272 + 153 + 72 + 57 = 899$

Step3: Compute the mean

Divide the weighted sum by total frequency, round to 2 decimals.
$\text{Mean} = \frac{899}{57} \approx 15.77$

Step4: Locate median position

Find the middle position of the ordered data set.
$\text{Median position} = \frac{57 + 1}{2} = 29$

Step5: Find the median age

Cumulate frequencies to find which age contains the 29th data point:
Cumulative frequencies: 5 (13), 10 (14), 24 (15), 41 (16)...
The 29th value falls in the age group 16.

Step6: Identify the mode

Find the age with the highest frequency.
The highest frequency is 17, corresponding to age 16.

Answer:

The mean is approximately 15.77 years.
The median is 16 years.
A. The mode is 16 years.