"Between 30 and 40 per cent of children attending school A had problems in the areas of spelling, listening, articulation and concentration in classes, while the equivalent/counterpart figures for school B stood at between 5 and 15 per cent."
I wonder if the two words "equivalent" and "counterpart" are interchangeable to each other here in the context as I checked up on the dictionary that the two words both means having same purpose or value as something else does.
No, they aren't interchangeable here. Neither of them work. Equivalent is an error and counterpart is being used in a nonidiomatic way, although the general sense of the word is appropriate to the sentence's objective. BoldBen's answer handles the counterpart issue.
Equivalent is used when establishing a comparison, not when establishing a contrast. So you can say
The test scores had different distributions—a score of 80 on test A being equivalent to an 83 on test B.
Here you are establishing differently-valued numbers as equivalent statistics.
Equivalence is about establishing interchangeability between easily distinguishable things. 1/2 and 2/4 are equivalent fractions. It doesn't work with contrasts because contrasting items are not interchangeable.
In a related question Equal vs equivalent ..., John Lawler wrote in a comment
... whereas equivalent means 'is a satisfactory substitute for'. And substitution requires a context.
Clearly, in the example statement, satisfactory substitute for is not the context.
The phrase equivalent figures is fairly common.
However, while the phrase counterpart figures is syntactically possible, I'd say it's so unusual that it's not something that should be considered if you want to sound natural.
Google Ngram Viewer indicates that counterpart figures is much less common—and it almost flatlines at the bottom of the usage chart, with only a slight increase around 1980 for some reason.
In short, keep to equivalent in this phrase and context.
The Cambridge Online Dictionary defines counterpart as
a person or thing that has the same purpose as another one in a different place or organisation
This means that 'counterpart' relates people, things or other entities to others of the same type. It does not, usually, relate characteristics of entities to each other.
Also if you look at the definition and examples in the Merriam Webster entry for 'counterpart' you will see the same thing but with more examples. For instance MW gives the example
The secretary of defense met with his counterparts in Asia to discuss the nuclear crisis.
That means you could say that "The figures for A's counterpart, B, were between 5 and 15 percent" and use counterpart in its normal way but that talking about "the counterpart figures for B" is definitely not standard.
Jason Bassford's answer includes an Ngram showing that there are a very few cases where the phrase 'counterpart figures' has been used in published work but I would suggest that many, if not all, of those are cases where 'figures' does not mean numbers, or indeed any characteristics of entities. I think they could easily be phrases such as "The great Impressionists and their counterpart figures from the Renaissance" or "The leaders of the Russian revolution such as Lenin and their counterpart figures in the Chinese communist revolution such as Mao"
In a comparison of statistics from two schools the correct term is "equivalent figures".
