
258 Ga. 75 (1988)
365 S.E.2d 111
ALDRIDGE
v.
THE STATE.
44863.
Supreme Court of Georgia.
Decided March 2, 1988.
Reconsideration Denied March 16, 1988.
Short & Fowler, James M. Bivens, Thomas S. Bishop, for appellant.
H. Lamar Cole, District Attorney, J. David Miller, Charles M. Stines, Assistant District Attorneys, Michael J. Bowers, Attorney General, J. Michael Davis, Assistant Attorney General, for appellee.
CLARKE, Presiding Justice.
Aldridge faces a life sentence after his conviction of the malice murder of Lorenzo Lamar. He was also convicted of possession of a firearm during the commission of a crime and was sentenced to a term of years. Three and a half days after the victim hit appellant in the head with a beer bottle during an altercation, the victim passed by appellant, who was sitting on his porch smoking marijuana laced with cocaine. The appellant chased the unarmed victim into a grocery store, cornered him behind the meat counter, and shot him. Appellant appeals from his conviction, enumerating three errors.
1. We find that the evidence here is sufficient to meet the requirements of Jackson v. Virginia, 443 U. S. 307 (99 SC 2781, 61 LE2d 560) (1979).
2. Aldridge contends the court erred in refusing to charge the jury as to voluntary manslaughter pursuant to a written request. We held in State v. Stonaker, 236 Ga. 1, 2 (222 SE2d 354) (1976): "The state or the accused may, by written application to the trial judge at or before the close of the evidence, request him to charge on lesser crimes that are included in those set forth in the indictment or accusation, and his failure to so charge as requested, if the evidence warrants *76 such requested charge or charges, shall be error."
This presents the question of whether the evidence supports a finding of provocation demanding a manslaughter charge. If the evidence of provocation was not sufficient, the court did not err in refusing to give the charge. Bowen v. State, 241 Ga. 492 (246 SE2d 322) (1978). Aldridge argues that the victim's hitting him in the face with a beer bottle was sufficient provocation to mandate a charge on voluntary manslaughter. However, three and a half days elapsed between the injury to appellant and the murder. Appellant contends that OCGA § 16-5-2 reserves the question of the cooling off period for the jury and that it cannot be considered by the court in assessing Aldridge's request to charge. "Although the jury is the judge of whether there was an interval between the provocation and killing sufficient for the voice of reason and humanity to be heard, it is a question of law for the courts to determine whether there is slight evidence that the defendant acted as the result of sudden, violent and irresistible passion resulting from serious provocation." Henderson v. State, 234 Ga. 827 (218 SE2d 612) (1975). The court could conclude as a matter of law that the incident did not constitute even slight evidence of provocation because of the three and a half day cooling off period between the incident and the killing. See Baker v. State, 238 Ga. 389 (233 SE2d 347), cert. denied, 431 U. S. 970 (1977). Therefore, appellant was not entitled to a manslaughter charge.
3. Appellant assigns error to the court's refusal to exclude statements given during custodial interrogation. He insists that because he did not sign a waiver of rights form before talking to police the statements were not freely and voluntarily given. It is undisputed that he was given Miranda warnings and that he at no time requested an attorney. The refusal to sign a waiver of rights form before speaking to police does not render the statements involuntary and inadmissible. Once Miranda warnings are given and a person in custody gives a statement to police without invoking his right to remain silent and without requesting an attorney, he has in effect waived his rights. The refusal to sign a waiver form does not constitute an invocation of the right to remain silent or the right to counsel. The trial court did not err in finding that the statements were freely and voluntarily given despite the refusal of appellant to sign the waiver. Mitchell v. State, 254 Ga. 353 (329 SE2d 481) (1985).
4. Aldridge contends his conviction must be reversed because the state used seven of its ten peremptory strikes to strike blacks from the jury and both of its peremptory challenges to strike blacks during the selection of alternate jurors. He claims that the state thus used its peremptory strikes in a racially discriminatory manner in violation of the mandate of Batson v. Kentucky, 476 U. S. ___ (106 SC 1712, 90 LE2d 69) (1986). The trial court ruled: "[t]he Court will take judicial *77 notice of the composition of the panels of Jurors. The Court will also take judicial notice of the fact that five of the fourteen Jurors selected in this case are black. That shows on its face and per se that there was no racial discrimination exercised by either party in this case. Consequently, the motion is overruled as Batson v. Kentucky would not be applicable in this matter." Aldridge insists that the case must be remanded for a determination whether the state had a racially neutral reason for the striking of each black juror.
This court directed the trial court to supplement the record showing the racial composition of the panels from which the jury was selected. The supplement reveals an inconsistency with defense counsel's statement to the trial court when he made the Batson motion. At that time he said his records indicated the state utilized nine of its ten strikes to remove black persons from the jury of twelve and both of its strikes to remove black persons from the alternate list. According to the supplement to the record, the state struck seven black persons and three white persons from the jury of twelve and two black persons from the alternate list. Defense counsel now stipulates the supplemented record to be correct. This emphasizes the importance of a complete record in cases involving the Batson issue. We hold that in the future the defendant in Batson type cases has burden to complete the record with information revealing the racial composition of the panel from which the jury was selected, the racial breakdown of the strikes of both parties, and the racial composition of the resulting jury.
Batson appears to establish a progression of legal exercises leading to the conclusion of discrimination vel non. The first is the right to rely on the fact that peremptory strikes offer the prosecution a potential tool for discrimination. Second, the defendant must show membership in a racially cognizable group and that the prosecution used peremptory strikes to remove persons of his race from the jury. Then the defendant is burdened with showing that these facts and other relevant circumstances raise an inference of the prosecution's racial motive in the use of peremptory strikes. From this exercise the court decides whether there is a prima facie case of discrimination. Batson v. Kentucky, supra, 106 SC at 1723. In this case the trial court found none.
On review we recognize the race membership of Aldridge as a black man. We note that the state used seven of its ten peremptory strikes to remove blacks from the jury and both of its strikes to remove blacks during the selection of alternate jurors. We know that the resulting jury, including alternates, was composed of nine whites and five blacks. But our inquiry concerning a prima facie case of discrimination does not stop here. Another factor lies in the background for possible consideration. In Batson, the U. S. Supreme Court added *78 the phrase "and other relevant circumstances" as a matter for consideration in deciding whether an inference of the prosecution's racial motive in the use of peremptory strikes has been raised. We therefore inquire into other relevant circumstances in this case. In doing so, we must travel a road of legal reasoning scantily mapped by the Batson opinion because it fails to define the circumstances or direct the manner of their application.
The supplemented record provides us with facts which constitute other circumstances. We must decide whether these circumstances are relevant and whether they affect the inference of a racial motive. The facts appear below.
Georgia law authorizes twenty strikes by the defense and ten strikes by the state in felony cases. OCGA § 15-12-165. Each party (state first and then the defense) has the right to strike each potential juror individually. OCGA § 15-12-167. Theoretically, the parties could seat a jury of twelve without any strikes being exercised, but, nevertheless, a panel of at least forty-two qualified jurors must be offered for consideration. When the court orders the seating of alternate jurors, the parties strike from a panel large enough to accommodate double strikes for the defense and still leave sufficient jurors to fill the authorized alternate positions. OCGA § 15-12-169.
In this case, the jury of twelve was struck from a panel of forty-two. The defense used all twenty of its strikes and the state used all ten of its strikes. The panel of forty-two contained thirty-two white persons and ten black persons (slightly less than 24% black). The alternate selection procedure used five prospective jurors, including four black persons and one white person (80% black). In selecting the jury of twelve, the state struck seven black persons and three white person (70% black). The defense struck twenty white persons and no black persons (0% black). This process resulted in a jury with three black persons and nine white persons (25% black).
In selecting the two alternate jurors, the state struck two black persons and no white persons (100% black). The defense in this process struck one white person and no black persons (0% black). This resulted in seating two black alternate jurors and no white alternates (100% black). These facts appear clearly by use of a table.


                              Black    White    % Black
Panel of 42 10 32 24
Jury of 12 3 9 25
Alternate list of 5 4 1 80 Two Alternates 2 0 100
Overall Panels 47 14 33 30 Overall Jury and Alternates 5 9 36



*79
State Strikes (jury of 12) 7 3 70 Defense Strikes (jury of 12) 0
20 0
State Strikes (Alternates) 2 0 100 Defense Strikes (Alternates) 0
1 0
State Strikes (overall) 9 3 75 Defense Strikes (overall) 0 21 0

The question then is whether this statistical data impacts upon the raising of the inference necessary to dictate a prima facie case of discrimination. We recognize the use of the phrase "other relevant circumstances" in Batson appears in a sentence dealing with an inference of racial motive. However, we also note that this inference is one which must lead to the result of discrimination. The result of the striking process in this case is interesting. Black persons composed exactly 25% of the jury of twelve, more than a percentage point higher than the panel of forty-two from which the parties selected the jury. Black persons composed 100% of the alternates while the list used for their selection contained 75% black persons. Hence, a net increase in the percentage of black persons occurred in both the jury of twelve and the alternates upon completion of the exercise of the peremptory strikes by each party.
Deciding cases through the use of raw numbers carries with it inherent dangers and possibilities of illogical or unjust results. We do not believe the U. S. Supreme Court intended to lead the courts into this kind of hazard. Using numbers as the only criteria under Batson would mean that if the panel of 42 was composed of 42 black persons, a prima facie case becomes automatic. In this case, the state's use of its strikes when considered in isolation might raise the inference of racial intent. But the larger question is whether it led to a prima facie case of discrimination. Viewing the resulting composition of the jury as an "other relevant circumstance," we cannot hold that it does. We agree with the trial court that no discrimination occurred.
Judgment affirmed. All the Justices concur.
