To determine how adding another age of 33 impacts the mean of the group of lifeguards, let's follow these steps:
1. Find the initial mean of the given ages:
The ages provided are:
[tex]\[
17, 17, 18, 19, 22, 23, 25, 27, 32, 38
\][/tex]
Calculate the sum of these ages:
[tex]\[
17 + 17 + 18 + 19 + 22 + 23 + 25 + 27 + 32 + 38 = 238
\][/tex]
There are 10 ages:
[tex]\[
\text{Number of ages} = 10
\][/tex]
Thus, the initial mean (average) is:
[tex]\[
\text{Initial mean} = \frac{238}{10} = 23.8
\][/tex]
2. Add the new age to the data:
When we add the age 33, the new list of ages becomes:
[tex]\[
17, 17, 18, 19, 22, 23, 25, 27, 32, 38, 33
\][/tex]
Calculate the new sum:
[tex]\[
238 + 33 = 271
\][/tex]
Now, there are 11 ages:
[tex]\[
\text{Number of ages} = 11
\][/tex]
3. Calculate the new mean:
The new mean is:
[tex]\[
\text{New mean} = \frac{271}{11} \approx 24.636
\][/tex]
Thus, when the age of 33 is added to the original data, the mean increases. The new mean is approximately [tex]\( 24.64 \)[/tex], which can be rounded to about [tex]\( 24.6 \)[/tex].
Therefore, the correct answer is:
- The mean would increase in value to about 24.6.
