
das Mittel
remedy
A substance or preparation used for a specific purpose, e.g. for healing, cleaning, or combating pests.
Gibt es ein wirksames Mittel gegen Mückenstiche?
Is there an effective remedy for mosquito bites?
remedy / means
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remedy
A substance or preparation used for a specific purpose, e.g. for healing, cleaning, or combating pests.
Gibt es ein wirksames Mittel gegen Mückenstiche?
Is there an effective remedy for mosquito bites?

means
A method, action, or approach used to achieve a specific goal.
Kommunikation ist das beste Mittel, um Missverständnisse zu vermeiden.
Communication is the best means of avoiding misunderstandings.

mean / average
The average value from a series of values; the middle value.
Das arithmetische Mittel von 2, 4 und 9 ist 5.
The arithmetic mean of 2, 4, and 9 is 5.

ways and means
A fixed expression meaning that one will find possibilities or methods to achieve something.
Wir werden Mittel und Wege finden, um das Projekt doch noch zu finanzieren.
We will find ways and means to finance the project after all.
'Das Mittel' (remedy/means) is closely related to 'die Mitte' (the middle). Figuratively speaking, a 'Mittel' is something that stands in the middle between a problem and a solution and helps you get from one to the other.
Dieses Medikament ist ein gutes Mittel gegen Kopfschmerzen.
This medication is a good remedy for headaches.
'Mittel' (remedy/agent) is often the second part of compound nouns. The first part describes the purpose, e.g. 'Schmerzmittel' (painkiller, against pain), 'Waschmittel' (detergent, for washing), or 'Lösungsmittel' (solvent, for dissolving).
Hast du ein gutes Waschmittel für bunte Wäsche?
Do you have a good detergent for colored laundry?
The idiom 'ein Mittel zum Zweck' (a means to an end) is very common. It describes an action or thing that is not good in itself, but is necessary in order to achieve a specific goal.
Für ihn war der Job nur ein Mittel zum Zweck, um Geld zu verdienen.
For him, the job was only a means to an end: to earn money.
The meaning 'Durchschnitt' (average) is used almost only in mathematical or scientific contexts. Watch for words like 'arithmetisch' (arithmetic) or the phrase 'im Mittel' (on average).
Im Mittel beträgt die Temperatur hier im Sommer 25 Grad.
On average, the temperature here in summer is 25 degrees.
possibility
Both expressions can refer to how one can achieve a goal. „Möglichkeiten“ focuses more on the available room for action, while „Mittel und Wege“ emphasizes the methods or solutions for achieving it. When the room for action is limited, „Möglichkeiten“ is the better fit; when looking for concrete solutions, „Mittel und Wege“ is more natural.

Für die Renovierung werden wir trotz des kleinen Budgets Mittel und Wege finden.
Despite our small budget, we will find ways and means to complete the renovation.
Für die Renovierung haben wir wegen des kleinen Budgets nur wenige Möglichkeiten.
Because of our small budget, we have only a few options for the renovation.