Answer :
We begin with the list of numbers:
[tex]$$
61,\; 57,\; 49,\; 60,\; 45,\; 5x,\; 57,\; 60,\; 53,\; 57,\; 55,\; 48,\; 65,\; 52.
$$[/tex]
Since the term [tex]$5x$[/tex] represents a two-digit number in the 50s, we assume that [tex]$5x = 50$[/tex]. With this assumption, our list becomes:
[tex]$$
61,\; 57,\; 49,\; 60,\; 45,\; 50,\; 57,\; 60,\; 53,\; 57,\; 55,\; 48,\; 65,\; 52.
$$[/tex]
Step 1. Sorting the List
Let’s sort these numbers in increasing order:
[tex]$$
45,\; 48,\; 49,\; 50,\; 52,\; 53,\; 55,\; 57,\; 57,\; 57,\; 60,\; 60,\; 61,\; 65.
$$[/tex]
The smallest number (i.e. the minimum) in this sorted list is clearly:
[tex]$$
45.
$$[/tex]
Step 2. Finding the Mode
The mode is the number that appears most frequently. Here, we count the occurrences of each number:
- [tex]$45$[/tex] appears once.
- [tex]$48$[/tex] appears once.
- [tex]$49$[/tex] appears once.
- [tex]$50$[/tex] appears once.
- [tex]$52$[/tex] appears once.
- [tex]$53$[/tex] appears once.
- [tex]$55$[/tex] appears once.
- [tex]$57$[/tex] appears three times.
- [tex]$60$[/tex] appears twice.
- [tex]$61$[/tex] appears once.
- [tex]$65$[/tex] appears once.
Since the number [tex]$57$[/tex] appears three times while no other number appears as frequently, [tex]$57$[/tex] is the mode.
Conclusion
Thus, the minimum value is [tex]$45$[/tex] and the mode is [tex]$57$[/tex]. The final answer is:
[tex]$$
\text{Minimum} = 45,\quad \text{Mode} = 57.
$$[/tex]
[tex]$$
61,\; 57,\; 49,\; 60,\; 45,\; 5x,\; 57,\; 60,\; 53,\; 57,\; 55,\; 48,\; 65,\; 52.
$$[/tex]
Since the term [tex]$5x$[/tex] represents a two-digit number in the 50s, we assume that [tex]$5x = 50$[/tex]. With this assumption, our list becomes:
[tex]$$
61,\; 57,\; 49,\; 60,\; 45,\; 50,\; 57,\; 60,\; 53,\; 57,\; 55,\; 48,\; 65,\; 52.
$$[/tex]
Step 1. Sorting the List
Let’s sort these numbers in increasing order:
[tex]$$
45,\; 48,\; 49,\; 50,\; 52,\; 53,\; 55,\; 57,\; 57,\; 57,\; 60,\; 60,\; 61,\; 65.
$$[/tex]
The smallest number (i.e. the minimum) in this sorted list is clearly:
[tex]$$
45.
$$[/tex]
Step 2. Finding the Mode
The mode is the number that appears most frequently. Here, we count the occurrences of each number:
- [tex]$45$[/tex] appears once.
- [tex]$48$[/tex] appears once.
- [tex]$49$[/tex] appears once.
- [tex]$50$[/tex] appears once.
- [tex]$52$[/tex] appears once.
- [tex]$53$[/tex] appears once.
- [tex]$55$[/tex] appears once.
- [tex]$57$[/tex] appears three times.
- [tex]$60$[/tex] appears twice.
- [tex]$61$[/tex] appears once.
- [tex]$65$[/tex] appears once.
Since the number [tex]$57$[/tex] appears three times while no other number appears as frequently, [tex]$57$[/tex] is the mode.
Conclusion
Thus, the minimum value is [tex]$45$[/tex] and the mode is [tex]$57$[/tex]. The final answer is:
[tex]$$
\text{Minimum} = 45,\quad \text{Mode} = 57.
$$[/tex]
