I think it's important to be careful when we analyze individual records because our own assumptions about what we should be seeing get in the way of our understanding what is actually there. Here are some things to consider.
We can't take records at face value.
The census record claims that Ellen is the grand-daughter of the head of household, but is that so? In the handout to his class Inferential Genealogy, Dr. Tom Jones, CG, CGL, FASG, FUGA talks about the difference between Kinship Acceptance and Kinship Determination. He defines the former as:
The uncritical use of kinships determined or accepted by others.
and he says:
Kinship acceptance is a convenient method of doing genealogy.
Relationships stated in records or published in family histories are
easy to accept, but are often wrong. Even records created in the
moment can contain misinformation if the informant was misinformed or
purposely provided false information. Instead of blindly accepting a
stated relationship, a genealogist should use kinship determination to
establish familial relationships; inferential genealogy is one method
of kinship determination.
The class handout and video of this class is available for viewing in the FamilySearch Learning Center.
One red flag that signals a lack of critical thinking is the shorthand of saying "this record proves X". Records don't prove our theories or hypotheses -- genealogists do, by writing convincing proof statements after gathering and analyzing a body of complex evidence. In any case, a single record is not enough to support an entire proof.
I have a copy of a will in a will book where the deceased left shares in his estate to two of his granddaughters. They were the daughters of the deceased's daughter; also mentioned in the will were his other two children, his sons, who acted as the executors. I might say in casual conversation that this record "proved" the relationship, but what really happened is that this will validated a theory I had formed from looking at many other records about this family, trying to confirm the sister's relationship to her brothers by indirect evidence.
An observer won't know whether I have proof of my kinship determination unless I write up a convincing proof statement and show that I did a good job in searching for records and analyzing them.
For another family, I have a funeral notice which lists all the bearers -- two of them are described as the nephews of the deceased. I 'know' from other evidence already assembled that the individuals named are more likely to be the deceased's grandsons.
Taken in isolation, there's no way to see whether the stated relationships in these two examples are right or wrong. It's easy to say that newspapers make mistakes, but so do enumerators.
In order to apply the techniques of Inferential Genealogy, we need more than a single record to look at. Comments on the original question indicate that a search for Ellen in other records has not been fruitful. I'll use this 1880 Census record as an example to demonstrate reasons why we might not find our person of interest in the records and how learning more about the records might help us.
When we do a search, we are searching for records, not people.
Everyone talks about "finding their grandparent in the census" -- but no, we really haven't. We have found a record which we think is something that refers to or belongs to our grandparent. This is a subtle distinction, but it can color the way we construct our search and prevent us from finding things. See Crista Cowan's video Smarter Searching: Look for Records Not People for examples of how people might block themselves.
Historical Records Were Created for Specific Purposes, mostly not for genealogy
When studying any record, ask yourself how much you know about the type of record and the purpose for which it was made. Although the census may show the names of individual people, it wasn't intended to be consulted to prove the identity of everyone, in the way that a modern voter registration roll might be. It was made for the purpose of population study, and to count people for reapportionment. Because of that, we can gain insight into the record by looking into the work of people who use the data for that purpose. We can also learn from the work of archivists who maintain custody of the records, because they have looked at far more individual examples from this collection that we do. Some useful resources are:
How Did This Census Record Get Online Anyway?
Another thing to consider is the lifespan of the records themselves -- when and how they were created, how they were microfilmed, and how the images are put online. FamilySearch cites the record we are looking at like this:
"United States Census, 1880," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MH6S-1GR : accessed 25 March 2016), Ellen M Berry in household of Alfred Magnal, Fall River, Bristol, Massachusetts, United States; citing enumeration district ED 104, sheet 253C, NARA microfilm publication T9 (Washington D.C.: National Archives and Records Administration, n.d.), roll 0524; FHL microfilm 1,254,524.
This tells us we are looking at a microfilm publication of a federal copy of the census which is held by the US National Archives and Records Administration (NARA). NARA's website has a huge amount of information for researchers who really want to dig into the records -- one entry point is their page 1790-1890 Federal Population Censuses which has links to finding aids, a bibliography to published works about the census, and more.
The article United States Census Historical Background in the FamilySearch Research Wiki gives an overview of the process. One consideration is that there may be other copies besides the Federal Copy we're seeing now. The article says:
Multiple copies. Three copies of most federal censuses were created. The local census taker first created a draft copy as he walked from house to house to question the residents. He later copied by hand a second draft for the state, and a third copy for the federal government. Copying errors often resulted in slight differences between the various copies. Only a few of the local or state copies have survived. Occasionally, large cities were enumerated twice in the same year when an under-count was suspected the first time.
So -- not all copies survive, but in a few cases, it is possible to go to a local archive or the state archives, and view the other copies of the census. Even if we can't, we need to be aware that the Federal Copy we're seeing via microfilm for a pre-1890 Census is probably not the same copy that the enumerator wrote down in the field.
How is the microfilm arranged?
Researchers should be aware of two issues with using microfilm instead of the original paper records and of the digital images of that microfilm which we use online.
There's no guarantee that the people who made the original microfilm captured all of the pages, or took the images in the same order as the paper records were arranged.
There's no guarantee that the digital images online are being presented to us in the same order that they appear on the microfilm roll. See footnote 10 in Elizabeth Shown Mills' QuickLesson 16: Speculation, Hypothesis, Interpretation & Proof where she warns that Ancestry's "has inaccurately rearranged pages of this census to create two (not five) arbitrary and misleading divisions" -- important to know if you are looking for relatives located nearby. The census pages may not reflect the neighborhood -- pay careful attention if you plan to retrace the steps of the enumerator.
But what about the index?
As noted in the question itself, FamilySearch's indexers missed the correction on the sheet and listed Ellen as a Daughter:
Any of these issues can affect whether or not we find a person in our search.
Making a Research Plan
What do we need to find a person? I like the metaphor used by Jessica Hopkins, an archivist at NARA's Kansas City branch. During a session at NARA's 2015 Virtual Genealogy Fair, she talked about the name plus the date plus the location as being components of a "three-legged stool". If you have all three, you are on a stable object -- if you only have one or two of the three, the stool isn't going to hold you.
Instead of jumping in right away to search, use the principles outlined in How can I determine what records are available in a particular locale? to see what record groups you might expect to find Ellen in. A good place to start is the article Massachusetts, United States Genealogy on the FamilySearch Wiki. When you go to FamilySearch, look at the catalog and do a place name search for your area, searching all jurisdictions so you can find records at the town level, the county level, the state level, and the federal level. Instead of just searching the historical records, try the Browse All Published Collections because not all collections are indexed yet. Search for the articles in the research wiki that describe the record collection you want to search, and search the sites of the agency that holds the original records to see if they have any finding aids or reference documents that talk about the records.
Work up a list of possible variations for names, and think of ways to search without using names at all. Write down specific questions that you'd like to know about the person, and then think about the records that might hold those answers. Make a formal 'client report' for yourself listing all the things you have already done, and spelling out what tasks you would like to undertake -- this will focus your thinking and help you pick up again if you can't complete your entire set of tasks in one research session.
Log all the searches you make, including the searches that don't work out, including the precise research terms you used to make the search. That way, if someone suggests a new search technique, you can see at a glance which things you have already tried, and where you have searched.
The following articles on the FamilySearch Wiki can help: