Basic Math Did Not Require Expert Testimony

First Circuit affirms the admission of “basic multiplication” testimony of an expert forensic chemist concerning “the average per-bag weights of marijuana” which was offered to show “how much marijuana had been sold over the life of the conspiracy”; the testimony qualified as lay testimony under FRE 701 and was not expert testimony under FRE 702 or unfairly prejudicial under FRE 403, in United States v. Sepúlveda-Hernández, _ F.3d _ (1st Cir. May 2, 2014) (No. 13-1339, 12-2301)

When numerical data is presented at trial, it may be helpful to provide a basic arithmetic or statistical summary for the jury. While the jury may be capable at doing the math, a witness may facilitate this process by presenting the results of their calculations. A recent First Circuit case considered whether math evidence was expert testimony under FRE 702 or lay testimony under FRE 701.

Trial Court Proceedings: Total Marijuana Sales Over The Conspiracy

In the case, defendant Sepúlveda-Hernández was a drug supplier who was charged with conspiring to possess with intent distribute amounts of cocaine and marijuana. At trial, an expert forensic chemist testified about "the average per-bag weights of marijuana contained in the small and large bags habitually sold at the drug point." No objection was made to this part of the testimony. The prosecutor then asked the chemist about other evidence that "at least 250 bags of each size were sold at the drug point every day over the life of the conspiracy." In particular:

[T]he prosecutor asked the witness to perform some basic multiplication. This included multiplying the weight that the witness had ascribed to a typical small bag by 250 (representing daily small-bag sales), multiplying the weight ascribed to a typical large bag by 250 (representing daily large bag sales), multiplying each of those subtotals by 365 (representing days in a year), and then multiplying each of those subtotals by nine (representing years of operation). The government elicited this testimony in an apparent effort to estimate how much marijuana had been sold over the life of the conspiracy.

Sepúlveda-Hernández, _ F.3d at _. The trial court overruled the defense objection to the multiplication evidence. After the defendant was convicted, he challenged this testimony on appeal as unfairly prejudicial and as improper expert testimony.

First Circuit Analysis: Admissible Lay, And Not Expert, Testimony

The First Circuit affirmed the admission of the testimony "permitting the chemist to perform simple multiplication." The circuit noted that the record was unclear whether the multiplication testimony was offered as expert or lay testimony.

The circuit acknowledged that the line between expert and lay testimony is often unclear. Sepúlveda-Hernández, _ F.3d at _ (citing United States v. Colón Osorio, 360 F.3d 48, 52-53 (1st Cir. 2004) ("The line between expert testimony under Fed. R. Evid. 702 . . . and lay opinion testimony under Fed. R. Evid. 701 . . . is not easy to draw . . . ."); see also FRE 701 ACN (2000 amendments) (noting that the Evidence Rules do "not distinguish between expert and lay witnesses, but rather between expert and lay testimony [so] it is possible for the same witness to provide both lay and expert testimony in a single case." )).

The circuit concluded the multiplication testimony was lay testimony:

[W]e have scant difficulty in concluding that Rule 701 is the better fit for simple multiplication of the sort that the chemist performed here. Lay opinion is generally thought to encompass information that can be deduced "from a process of reasoning familiar in everyday life." Fed. R. Evid. 701 advisory committee's note on the 2000 amendments (internal quotation mark omitted). Simple arithmetic, such as ordinary multiplication, is a paradigmatic example of the type of everyday activity that goes on in the normal course of human existence. One does not need a graduate degree in chemistry to master multiplication: in this country, that subject is universally taught in elementary schools. Without such a rudimentary skill, ordinary tasks such as figuring a family's budget, shopping in a supermarket, and converting a recipe for four into a meal for ten would assume Herculean proportions.

Sepúlveda-Hernández, _ F.3d at _. The circuit also rejected the defendant's argument that the math testimony was unfairly prejudicial under FRE 403:

The foundational quantity-and-time evidence relied on by the government was in the record. Although these facts were not gospel — it remained for the jury to decide whether to accept or reject them — the direct examination was carefully phrased so that the chemist, by doing the requested multiplication, was not vouching for components such as how much business was transacted at the drug point or how long the conspiracy lasted. And the defense was free to build its own theory, asking the chemist on cross-examination to multiply by smaller numbers or fewer years. It did not exploit this opportunity.

Sepúlveda-Hernández, _ F.3d at _.


The Sepúlveda-Hernández case shows that basic math may be admissible as lay testimony. For other cases touching on this issue, consider:


Photo Description: First Circuit Court of Appeals, John Joseph Moakley United States Courthouse, Boston, Massachusetts. Learn more about this courthouse here.


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