Due to this comment...
would prefer knowing how strong they'd be if they were proportionately as strong as a regular mermaid
This answer shall now proceed to give information that disregards these statements.
You see, a little mermaid has enhanced strength; the strength of a typical mermaid packed inside a sardine-size frame. In other words, despite their size, they have the same strength as a regular-sized mermaid, and since they don't need to use most of that strength to move or support a large body, they can channel it into ridiculous feats
Little mermaid strength = normal mermaid strength, proportionately
Probable body weights of LM(little mermaid) vs NM(normal mermaid)...
You see, mermaids in my setting are capable of extreme dwarfism. How extreme? Well, if you've ever seen a sardine, or perhaps a neon tetra, that should give you a good idea.
The weight of sardine in Washington's fishery can be as small as 80 grams and as large as 300 grams but the average weight of sardine in our fishery is 150-175 grams. link
A Mermaid isn't a half-human, half fish. It is a human-orca-fish trifold chimera. -> accepted answer -> Human half will be focused on for strength determining purposes but weight will factor in
Many other events are listed between these examples and a number of events are found to share the same combination of height and weight (height 171 cm, weight 59-62 kg) swimming freestyle -> Age, height and weight of female Olympic finalists
... LM = 150g vs NM = 100kg(added weight for NM from orca-like aquatic tail, conservative and round approximation, bottlenose dolphins weigh 150-200kg so it's not like I'm making them fat)
Determining strengths... Focusing on female statistics due to female body specificity of previous questions...
The average woman should be able to deadlift a bit more than she can squat, at between 100% to 125% of her overall body weight
the average woman can only bench press between 50% and 75% of her total body weight.
women can squat near as much as they can deadlift. So the average woman is likely able to squat between 75% to 125% of her body weight.
Punching forces in amateur boxing are around 2500 N. If you weigh 70 kg (11 stone or 154 lbs), you’ll exert about 700 N of force on the ground just stood still. That makes punching force about 3.5 times body mass.
link... data specifically on average(non-boxer) females seems non-existent, or I'm blind, either way I tried to find it
For the purposes of this question I'll be translating average squat power into tail-only-ability-to-lift-things-upwards-underwater, TOATLTUU. Dead lifts will be halved due to only the upper body contributing to the lift, but being underwater may affect this number and have them be able to lift slightly more, incorporating the tail in this will help while underwater but it might as well be a mermaid squat at that point, see TOATLTUU for figures involving tail incorporation.
100kg NM approximate averages:
- Dead lifts, 50-62.5kg - Upper body alone can lift very light humans
- Bench press, 50-75kg - Arms are capable of holding up average but skinny humans
- TOATLTUU, 75-125kg - Tail incorporation underwater allows the lifting up of heaver kinds of human, assuming the weren't buoyant(dead weight) and sank
Punch force, assuming your mermaids had the training of average boxers and could transfer the forces in a similar way while staying in one spot, 3500N. Swimming quickly will add to punch force as running does, (F = M x A) and all that.
University of Southern California estimates that a force of 3,300 newtons has a 1 in 4 chance of cracking the average person's rib
Congratulations, your normal mermaids are rib breakers, if they had boxer training.
150g LM approximate averages:
- Dead lifts, 75-94.75g - A pack of crisps will be a great undertaking and will probably fail.
- Bench press, 75-112.5g - That pack of crisps might just get held aloft.
- TOATLTUU, 112.5-187.5g - Guaranteed crisp packet movement.
Punch force, assuming your little mermaids had the training of average boxers and could transfer the forces in a similar way while staying in one spot, 5.25N. - Might be good for tickles
If, however, you really, really want to pack the strength of a normal mermaid into a little mermaid...
They'll be able to move as much mass as a normal mermaid(assuming they can get a good enough and well-balanced grip), but take care that they don't try it with things as squishy as humans, unless you want them as combatants. They're more likely to pierce human flesh than help them in any regard from the combination of their strength and the amount of surface area they apply it through, and for that matter will be asolutely horrific against anything living, ripping and tearing everything they come across that doesn't happen to be made of bone or something much harder than flesh.
At least their swimming speed won't be too different(strength doesn't mean speed, you need more/better fast twitch muscles if you want them to be faster).