Plaintiff-Appellant Melinda. Hamilton (“Hamilton”), a former employee of AVPM Corporation, initiated an action in Texas state court against AVPM Corporation and Waters Landing Apartment (collectively, “AVPM”), asserting claims of race and age discrimination in violation of Title VII of the Civil Rights Act of 1964, 42 U.S.C. § 2000 et seq., and the Age Discrimination in Employment Act of 1967 (“ADEA”), 29 U.S.C. § 621 et seq. AVPM removed the case pursuant to 28 U.S.C. §§ 1331 and 1441. The district court later granted AVPM’s summary judgment motion on both of Hamilton’s claims. Hamilton appeals the district court’s grant of summary judgment on her race discrimination claim1 on the grounds that the court overlooked genuine issues of fact in its summary judgment ruling, and that it mistakenly excluded relevant evidence. Finding no error, we affirm.
I. FACTS AND PROCEEDINGS
AVPM owns and operates nineteen apartment complexes in the DallasFort Worth area, including Waters Landing in Fort Worth, Texas. At each complex, the company employs a property manager, ad*317ministrative staff, and maintenance staff; additionally, AVPM employs property supervisors, each with oversight responsibilities over a group of complexes. Hamilton began working for AVPM as the assistant property manager at Waters Landing in April 2010. In January 2011, she was promoted to the position of property manager of that same complex. Laura Eaton, the property supervisor who oversaw Waters Landing, was responsible for hiring and promoting Hamilton. In May 2011, Eaton sought a reduction in the number of apartment complexes under her jurisdiction, and subsequently, Robert Englard assumed supervisory duties over Waters Landing and several other AVPM properties in the Fort Worth area.
Englard visited Waters Landing soon after to meet -with Hamilton and her staff. During that visit, he commented to Hamilton that everyone in the grounds crew was African American. Hamilton, who is also African American, responded by asking if that would be a problem, to which Englard looked “amazed” but otherwise made no reply.
As property manager, Hamilton was responsible for maintaining two lists: (1) vacant apartments that were “ready” for leasing/move-in, and (2) vacant apartments that she and the maintenance crew needed to “make ready” for leasing/move-in. These lists were the “bible” of the apartment complex, and particularly critical when showing vacant units to prospective tenants. During Hamilton’s tenure as property manager at Waters Landing, the complex had the highest vacancy rate of any of the nineteen AVPM properties.
Either during Englard’s initial visit to Waters Landing or one shortly thereafter, he and Hamilton walked around the apartment complex and visited several vacant units that were marked as “ready.” However, at least one “ready” apartment was, in fact, not ready.2 When Hamilton went on vacation in June 2011, Englard visited Waters Landing again and found more inaccuracies in the “ready” and “make ready” lists. Englard decided that he could no longer trust Hamilton to perform the duties of a property manager, and he fired her after she returned to work.
AVPM provided all employees with an employee manual that contained, inter alia, a description of the company’s internal disciplinary policy, and a statement that all workers were employed at will, subject to termination at any time with or without cause or advance notice. The disciplinary policy defined the types of actions that “may be taken in response” to violations of AVPM standards, including oral warnings, written warnings, and immediate termination. Neither Eaton nor Englard had documented any warnings in Hamilton’s employee record before she was terminated. Both stated that they had also fired Caucasian property managers without providing written warnings.
Hamilton and Eaton had three relevant conversations about AVPM. The first occurred when Eaton called Hamilton immediately after Eaton was fired as a property supervisor, and she bemoaned AVPM’s hiring of “bubbly white little girls” to fill management positions.3 Eaton was rein*318stated in her position three days later. The second and third conversations took place after Robert Englard fired Hamilton. At that time, Eaton was a property supervisor, but she no longer oversaw Hamilton or Waters Landing. In the second conversation, Eaton implied that race played a factor in Hamilton’s termination, noting that AVPM might have been concerned about friction between Hamilton and the entirely African American grounds crew at Waters Landing. In the third conversation, Eaton told Hamilton that AVPM had realized it had fired Hamilton “for no reason,” and asked if the company had contacted Hamilton about returning to work.4
Following her discharge, Hamilton filed this lawsuit, alleging race discrimination under Title VII and age discrimination under the ADEA. AVPM filed a motion for summary judgment, and in its reply brief, also lodged four evidentiary objections to statements used by Hamilton in her opposition to the motion. The district court sustained all four objections and granted AVPM’s motion for summary judgment on both counts. Hamilton appeals, claiming that (1) the court erred in sustaining AVPM’s objections, and (2) an issue of fact exists as to whether AVPM’s reason for terminating her is pretext for race discrimination. We have jurisdiction over Hamilton’s appeal of the district court’s judgment under 28 U.S.C. §§ 1291 and 1331.
II. ANALYSIS
A. Standard of Review
We review de novo the district court’s grant of summary judgment.5 In doing so, we consider the record as a whole, without weighing the evidence or making credibility determinations, and “draw all reasonable inferences in favor of the nonmoving party.”6 A party is entitled to summary judgment if “there is no genuine dispute as to any material fact and the moving party is entitled to judgment as a matter of law.”7 A genuine dispute of material fact exists when the “evidence is such that a reasonable jury could return a verdict for the nonmoving party.”8 We review evi-dentiary rulings for manifest error.9 Our practice has been first to “review the trial court’s evidentiary rulings, which define the summary judgment record,” and then to review the “summary judgment decision de novo.”10
B. Evidentiary Rulings
In its summary judgment opinion, the district court excluded four items of evi-*319denee relied on by Hamilton in her briefing before that court. The first was a statement made by Robert Englard during his deposition; the other three were statements allegedly made by Laura Eaton to Hamilton, as repeated by Hamilton in her own deposition. Hamilton contends that all four statements were excluded in error.
1. Englard’s Deposition Statement
Hamilton challenges the district court’s exclusion of Robert Englard’s statement about hypothetical racial bias. During Englard’s deposition, Hamilton’s counsel asked about Englard’s earlier comment to Hamilton that the entire grounds crew at Waters Landing was African American. Although Englard denied making the comment, he agreed with Hamilton’s counsel that it was possible for “someone” who heard such a comment to think that the hypothetical speaker “might” have racial bias. We agree with the district court: “Englard’s comment about how some unnamed, hypothetical person might perceive his remark is pure speculation.”
Under Federal Rules of Evidence 602 and 701, lay testimony must arise from the witness’s “personal knowledge of the matter” 11 and be “rationally based on the witness’s perception.”12 Indeed, the Advisory Committee explains .Rule 701(a) as the “familiar requirement of first-hand knowledge or observation.”13 We also require that lay opinion testimony be “helpful to the jury.”14
Nowhere does Englard, as Hamilton contends, assert his own opinion as to the meaning of the comment or make an admission regarding his own state of mind when allegedly making it. His testimony about the hypothetical “someone” has no basis in his own perceptions, observations, or knowledge. Furthermore, his opinion as to what “someone” might think is not helpful to the factfinder. The relevant issue is whether Englard acted with racial bias, not whether “someone” else might think him to be racist. Englard’s speculation as to that hypothetical listener’s state of mind is irrelevant and unhelpful. We conclude that the district court made no manifest error in excluding this testimony.
2. Hamilton’s Deposition Testimony About Eaton’s Statements
Hamilton also challenges the district court’s exclusion of three statements, made during her own deposition, that she attributed to Laura Eaton, her former manager at AVPM. The first statement allegedly occurred immediately after Eaton had been fired from AVPM. According to Hamilton, Eaton lamented the difficulty of “get[ting] another job at [their] age” and faulted AVPM for hiring “bubbly white little girls.” Eaton’s second statement also occurred during a conversation between Hamilton and Eaton, this time after Hamilton’s termination. In it, Eaton implied that Hamilton’s termination was motivated by race — specifically, that AVPM had concerns about the African American grounds crew at Waters Landing, who “couldn’t intimidate [Hamilton] like they’re used to doing with other women that don’t speak up.” Eaton’s third statement occurred a few days after Hamilton’s termination, when Eaton called to tell her that the company discovered it had fired her “for no reason.” According to Hamilton, Eaton then asked if AVPM had contacted Hamilton about returning to work. The district court excluded all three statements as inadmissible hearsay. *320It also excluded the first two statements as speculation and the third for lack of foundation.
Hamilton claims that Eaton’s statements are not hearsay as provided in Federal Rule of Evidence 801(d)(2)(D).15 However, “[u]nder our general rule, arguments not raised before the district court are waived and will not be considered on appeal unless the party can demonstrate ‘extraordinary circumstances.’ ”16 We find extraordinary circumstances when “the issue involved is a pure question of law and a miscarriage of justice would result from our failure to consider it.”17 Hamilton failed to respond to AVPM’s objections before the district court and makes no argument before us as to extraordinary circumstances, thus waiving this theory on appeal.18
C. Summary Judgment
1. Title YII Framework
We evaluate Title VII race discrimination cases using a modified McDonnell-Douglas approach.19 Hamilton must first establish a prima facie case of discrimination. The burden of production then shifts to AVPM to articulate a legitimate, nondiscriminatory reason for her discharge. If it does so, Hamilton must then show either that the proffered reason is pretext for discrimination or that AVPM acted with mixed motives, one of which was discriminatory. Hamilton has not argued before this court or the district court that AVPM acted with mixed motives. Thus, to avoid summary judgment, Hamilton must produce “substantial evidence” that the proffered legitimate, nondiscriminatory reason articulated by AVPM is false or unworthy of credence, and therefore pretext for discrimination.20
2. Legitimate, Nondiscriminatory Reason
On appeal, AVPM does not dispute that Hamilton has established a prima facie case of race discrimination.21 We therefore start with the second step of the *321McDonnell-Douglas framework and consider if AVPM has articulated a legitimate, nondiscriminatory reason for terminating Hamilton’s employment.
AVPM contends that they discharged Hamilton because she “repeatedly list[ed] apartments as ready to lease when in fact they were not ready.” As a result, Robert Englard no longer trusted her to do her job effectively. Hamilton contends that this reason is not legitimate because AVPM did not follow its internal disciplinary policy. According to Hamilton, only employees guilty of a “serious” violation would be terminated -without documented warning, and the policy’s list of serious violations did not include Hamilton’s alleged transgressions. Thus, Hamilton reasons, because “the guidelines demonstrate what the employer thought was a legitimate non-discriminatory reason for termination,” any reason not listed must by definition be illegitimate.
Hamilton’s reasoning is flawed. She does not dispute that she was an employee at will, subject to dismissal for any reason not statutorily prohibited. Indeed, she concedes that AVPM’s guidelines do not constrain its discretion to make employment decisions: She could be terminated for “good cause, or bad cause, or no cause at all.”22 Furthermore, even if we accepted Hamilton’s premise, she does not — and indeed, cannot — contend that the list in the employee manual is exclusive. In fact, the manual defines serious violations as “drug policy violation, sexual harassment ... destruction of company property, etc.”23 That et cetera contains a multitude of sins. An employer’s belief that she repeatedly failed to perform a critical job function, even if erroneous, would nonetheless justify her immediate termination under this provision. Because Englard’s dissatisfaction with Hamilton’s job performance would have been a legitimate, nondiscriminatory reason for discharging her, we affirm the district court’s determination that AVPM satisfied its burden of production.
3. Pretext
Accordingly, we now turn to the third step of the McDonnell-Douglas framework and consider whether there is a genuine dispute of material fact that AVPM’s reason for terminating Hamilton was pretext.24 Hamilton contends that (1) AVPM’s failure to follow its internal disciplinary policy when terminating Hamilton, (2) AVPM’s inconsistent explanations for Hamilton’s termination, (3) AVPM’s desire to reinstate Hamilton after realizing that her discharge was for no good reason, and (4) Englard’s comment about the grounds crew being African American, all demonstrate that the company’s proffered reason is pretextual.
a. Disciplinary Policy
First, Hamilton claims that AVPM failed to follow its internal disciplinary policy when terminating her, and that this failure demonstrates the pretextual nature of the termination. Although an “employer’s failure to follow its own policies may be probative of discriminatory intent,”25 we require discharged employees in discrimination eases to show, in addition, that they were treated differently from non-minority employees.26 We insist on this additional *322evidence because “Title VII does not protect employees from the arbitrary employment practices of their employer, only their discriminatory impact.”27 Hamilton offers no evidence suggesting that AVPM followed the internal disciplinary policy with non — African American employees and deviated from it in her case only. In fact, Englard stated that he also terminated three Caucasian property managers at AVPM-owned complexes for performance issues, none of whom received a written warning. Eaton testified to similar effect as to property managers under her supervision. Accordingly, AVPM’s failure to follow its internal disciplinary policy does not create a factual issue as to the falsity of its proffered reason for discharging Hamilton.28
b.Inconsistent Explanations
Second, Hamilton insists that AVPM submitted inconsistent explanations for terminating her, and that the district court erred in finding no evidence of pretext in this inconsistency. At various points, AVPM gave three reasons for firing Hamilton: (1) inaccuracy in listing apartments as “ready,” (2) inability to do the job, and (3) lack of trust to do the job. Although Hamilton is correct that inconsistency could suggest pretext,29 no such inconsistency exists here. The district court aptly characterized these explanations as different only as to them level of generality. At the highest level, AVPM did not trust Hamilton to do the job of property manager. On a lower level, Englard distrusted her because he believed that she was unable to do the job correctly. And at the lowest level of generality, the reason he thought her incapable was her failure to keep accurate “ready” and “make ready” lists. There is no inconsistency, and thus no evidence of pretext, in AVPM’s proffered legitimate, nondiscriminatory reason for terminating Hamilton.
c. Reinstatement
Third, Hamilton relies on Eaton’s statement that Hamilton was fired for “no reason” and may be asked back to AVPM as evidence undermining AVPM’s stated reason for terminating her. However, the only basis for this assertion is inadmissible hearsay, as explained above. Thus, we do not consider it when reviewing a grant of summary judgment.30
d. Englard’s Comment
Finally, Hamilton contends that Englard’s comment about the race of the grounds crew at Waters Landing is evidence of racial bias. In her deposition testimony, Hamilton claimed that Englard had, when he first visited the Waters Landing apartment complex, observed to her that the entire grounds crew was African American.31 Although Englard denies *323the exchange took place, we make all reasonable inferences in favor of the nonmov-ant when reviewing a grant of summary judgment.
Because Hamilton has failed to produce substantial evidence of pretext, we apply this court’s “stray remarks” doctrine to Englard’s comment.32 A remark is evidence of discrimination if it is (1) related to the protected class of which the plaintiff is a member, (2) proximate in time to the adverse employment action, (B) made by an individual with authority over that action, and (4) related to that action.33 “Comments that do not meet these criteria are considered ‘stray remarks’ and, standing alone, are insufficient to defeat summary judgment.”34
Englard’s comment satisfies the first three elements of the stray remarks test: (1) it relates to Hamilton’s race, as she and the grounds crew are all African American, (2) it occurred shortly before she was fired, and (3) it was made by Englard, who both parties agree was the primary deci-sionmaker behind Hamilton’s discharge. However, there is no evidence that En-glard’s observation about the race of the grounds crew was related to the decision to terminate Hamilton. Thus, Englard’s comment is insufficient to raise an issue of fact as to whether AVPM’s stated reason for terminating Hamilton was pretext for race discrimination.
III. CONCLUSION
Hamilton fails to point to sufficient summary judgment evidence to create a genuine issue of material fact as to whether AVPM’s proffered reason for terminating her was pretext for race discrimination. Thus, AVPM is entitled to summary judgment as a matter of law. The district court’s grant of AVPM’s motion for summary judgment is AFFIRMED.