The firm tracked prices on 110 items over five weeks at a Whole Foods location in Princeton, N.J., to find that, on average, prices are down 1.2 percent since Amazon finalized its $13.7 billion purchase of the grocer. (Jeffrey P. Bezos, the founder and chief executive of Amazon, owns The Washington Post.)

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And although Amazon offered discounts on a number of items right away, some of those prices have crept back up, according to the data. The price of frozen foods, for example, was 7 percent higher on Sept. 26 than on Aug. 28, when Amazon officially took over. Snack items had risen 5.3 percent in that period, while dairy and yogurt were up 2 percent. (Among categories where prices are lower: Beverages, down about 2.8 percent; bread and bakery, down 6.8 percent; and produce, down 0.5 percent.)

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Amazon did not immediately respond to requests for comment.

Whole Foods — nicknamed by some as “whole paycheck” — has struggled for years to shed its reputation as an overpriced purveyor of food. The company’s prices have historically been about 15 percent higher than at the average grocery store, according to Morgan Stanley.

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Amazon seized on that long-standing customer complaint by announcing that its first move would be to cut prices. From the beginning, the company said customers would see a series of discounted staples at local stores: Extra-large brown eggs for $3.19 instead of $3.49, organic apples for $1.99 a pound instead of $2.99, and Haas avocados for $1.49 apiece instead of $2.

It was no mistake, analysts said, that many of the markdowns were on everyday items that families tend to buy on a regular basis. The average shopper, they said, is more likely to notice a lower price on a carton of eggs than they are on a tin of anchovies.

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“The whole game is that you want the 100 most recognizable things — milk, apples, bananas — to be cheaper,” said Jan Rogers Kniffen, an industry consultant and former department store executive. “If you can do that, you can build a perception that the whole store is competitively priced.”

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It’s a model, he says, that Walmart, which is Amazon’s biggest competitor in the grocery space, has fine-tuned over the years. And there are signs that the publicity surrounding the markdowns was enough for some customers to give Whole Foods another chance. Data from location-based app Foursquare found a 25 percent increase in shoppers in the days after the Amazon takeover.

“The bottom line is, the lower prices got people into their stores,” said Phil Lempert, a California-based food industry analyst known as the “supermarket guru.” “People who hadn’t been there in years were suddenly thinking, maybe I should give it a try. This was a clear sign to shoppers — and the industry — that Amazon is serious about fixing things up.”

The Whole Foods deal has already been lucrative for Amazon. Since the takeover, Whole Foods has generated $1.6 million in sales through Amazon.com and its services, including Amazon Fresh and Prime Now, according to e-commerce analytics firm One Click Retail. (During the first week, Whole Foods products were so popular on Amazon that 93 percent of them sold out, according to One Click Retail.) Among the most popular purchases: turkey deli meat, coconut water and frozen vegetables.

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But the data from Gordon Haskett also show that while some prices are lower, others have gone up. Of the 110 items the firm tracked, prices decreased for 17 items and increased for 16 items. The vast majority of prices — on 70 percent of the items — remained the same.

The items that were discounted, such as breads baked in-house and selections from Whole Foods’ private label brand 365, often have higher profit margins and more wiggle room for markdowns, Lempert said. Items like frozen foods — a category where prices have climbed since Amazon took over — are more difficult to discount, he said, because they must be kept cold both in store and during transit.

“Frozen foods — which is a declining category anyway — uses the most energy of any department in the store,” he said. “It’s much easier for Amazon to say, ‘We’ll charge less for bananas.'”

But, industry analysts said, the grocery business is a notoriously difficult one with slim profit margins. Lowering prices in one area often means having to make up for those discounts elsewhere.

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“Like all grocery stores, if prices are lowered someplace, prices are raised someplace else,” said David J. Livingston, a supermarket analyst for DJL Research. “The over change is nil. Just like when a grocer claims to have lowered 5,000 prices. What they don’t tell you is they raised prices on 45,000 items to pay for it.”