
351 So.2d 1311 (1977)
Paul S. GRAFFEO
v.
CITY OF NEW ORLEANS and Civil Service Commission of the City of New Orleans.
No. 8846.
Court of Appeal of Louisiana, Fourth Circuit.
October 18, 1977.
*1312 William M. Detweiler, New Orleans, for plaintiffs-appellants.
Many, Lo Coco & Dwyer, Ralph D. Dwyer, Jr., New Orleans, for defendants-appellees.
Before LEMMON, GULOTTA and SCHOTT, JJ.
LEMMON, Judge.
Plaintiffs, four sergeants in the New Orleans Police Department, filed this suit seeking to require that their names be placed on the promotional register of policemen eligible for promotion to the rank of lieutenant. The trial court dismissed the suit, and plaintiffs appealed.
In the trial court plaintiffs' two-pronged attack on their exclusion from the register was based on assertions that (1) the Civil Service examination which they failed by one point was outdated and irrelevant to the position for which it was used as a test, and (2) the selection of the critical (passing) score was arbitrary and discriminatory. The issue in this court is the sufficiency of plaintiff's proof of these assertions.
On March 22, 1975 approximately 130 applicants were given the written examination, which was announced to be weighted 60% of the total score.[1] During the protest period immediately after the test a large number of protests were filed, both as to individual questions and as to the test material as a whole. Two of the 150 questions were eliminated and two more were rekeyed, *1313 and the candidates were graded on their answers to 148 questions. In early May the Chief of the Recruitment Division and his staff met, examined the test results, and set the critical score at 116 after discussing relevant factors. Because of litigation unrelated to this suit, the scores were not promulgated until October, 1975. Plaintiffs, each of whom had scored 115 on the examination, then filed this suit.
Content of the Examination
The announcement of the Civil Service examination contained the following statement:
"A written test, weighted 60%, designed to measure the candidate's knowledge of police procedures and practices, laws, municipal administration, community problems, government and related subjects. This test may also include parts designed to indicate the candidate's intelligence, judgment, educational level and relationships with the public, the employer and fellow employees."
Plaintiffs complain that they prepared for the examination by studying Department training keys and recent judicial decisions relating to law enforcement and that the test was taken entirely from a book of sample questions which was designed for candidates preparing for Civil Service testing in the general area of Police Science Advancement and which contained some terminology not normally used in this metropolitan area.
The purpose of the examination was to assist in selecting the most qualified men for the promotion by determining the candidates' level of intelligence, judgment, experience and knowledge of police science. There is evidence that some terms unfamiliar in this locality were used (since the book was prepared for nation-wide distribution), and perhaps the questions should have been revised to employ terms locally used. Also the sociologically oriented test might arguably be considered "better" if input from the Police Department had been sought in order to orient the questions more practically to the qualifications of the particular job.[2] However, this is an area in which courts should be slow to intrude, in the absence of arbitrariness or discrimination. Here, there was no showing that the test was not suitable to achieve the purpose for which it was administered, and more importantly there was no showing of a conflict between the book from which the testing materials were extracted and the Department training keys or other materials normally used by the applicants in studying for the examination.
We conclude plaintiffs failed to prove the examination fell below the requirements for promotion only after certification "under a general system based on merit, efficiency, fitness, and length of service". La.Const.1974, Art. 10, §§ 7, 17.

Arbitrariness and Discrimination in Setting the Critical Score
Plaintiffs contend that the setting of the critical score was arbitrary and discriminatory. They point out that the median was 112, that plaintiffs scored above the median, and that there were logical breaks in the curve but not at the 116 score.[3]
The setting of the critical score in this case was not controlled by Commission rules or fixed standards, but involved the exercise of judgment and discretion. The *1314 decision cannot be considered arbitrary unless the setting was made without reasons or reference to relevant considerations. Arbitrariness is the absence of a rational basis.[4]Bicknell v. United States, 422 F.2d 1055 (5th Cir. 1970).
John Belsom, the Chief of the Recruitment Division, testified that he and his staff not only considered the median and the frequency distribution, but also weighed other factors bearing on the desirable number to be placed on the register, such as the number of existing vacancies, the estimated number of additional vacancies expected to occur within the period of time the list was to remain in effect, the likelihood that vacancies would be filled, and the fact that a large percentage of candidates on the preceding register had not been promoted when that register expired.
Ten vacancies existed at the time of the examination, and Belsom stated he expected about 20 more during the effective period of the register. Although previous registers had customarily been kept in effect for the entire three-year maximum period prescribed by law, the Superintendent of Police had requested that this register be limited to two years. And on the last register containing 49 names, over half had not been promoted when the register expired in three years. (There were only four vacancies when that register was promulgated, but the record does not show how many vacancies were anticipated during the life of the register).
Belsom further testified that he kept a running tally of vacancies in the police and fire departments, that he was periodically furnished with current information on strengths and expected retirements, and that he was aware of the Superintendent's practice of allowing vacancies to remain open in order to generate money for overtime pay. He also pointed out that every person placed on the register had to be examined by a citizen interview board, a practical consideration suggesting thoughtful limitation of the number placed on the register. He decided, based on all of these considerations and on the frequency distribution, to cut below the score of 116, leaving 40 candidates to be placed on the register.
We do not deem this decision to be arbitrary, since there were many valid factors considered in reaching the decision. Furthermore, the critical score of 116 does not appear out of line when the frequency distribution is considered in the light of these factors, and we conclude there is no showing of an abuse of discretion.
As to discrimination, plaintiff Graffeo immediately after the examination directed a letter of protest to the Director of Civil Service, complaining of the materials used to compose the examination, the irrelevancy of the questions drawn from the source text, and the misleading information in the announcement. He testified that, after the test results were promulgated, Belsom stated he was "very familiar" with Graffeo's letter and would not promote Graffeo if it were his decision. Belsom denied making such a statement.
Graffeo's case as to discrimination (and the cases of the other three plaintiffs who failed, if the crucial score was set at 116 purposefully to eliminate Graffeo) is based primarily on circumstantial evidence. The circumstancesthat Graffeo's letter inferentially criticized Belsom, who was supervisor of the person that composed the test; that Belsom had access to the answer sheets containing the names and scores of each candidate; and that Belsom made the decision to cut off the passing grades just above Graffeo's scoreraise the inference of discrimination. However, these circumstances do not show that, more probably *1315 than not, discrimination actually occurred.[5] Moreover, while the statement alleged by Graffeo to have been made by Belsom might tip the preponderance, Belsom denied the statement, and we must assume the trial judge resolved this conflict against Graffeo. And we further assume that the judge accepted Belsom's testimony that he did not see any individual answer sheets before setting the crucial score.[6]
We conclude that plaintiffs have failed to establish discrimination.
The judgment is affirmed.
AFFIRMED.
NOTES
[1]  The remaining 40% weight of the total score was based on experience and a personal interview. However, only those who attained the minimum raw score on the written test were eligible for the register, and a candidate's total score (which determined his rank on the register) was determined by adding the weighted score on the written test to the weighted score based on experience rating.
[2]  The job-relatedness requirement of the federal cases cited by plaintiffs involves the burden of proof on the defendant to show that testing or eligibility requirements are job-related, a burden which is imposed only after a prima facie showing of racial discrimination.
[3]  The frequency distribution in the area of the critical score was as follows:



  Score     Number      Score        Number
   120        5          115           5
   119        4          114           4
   118        0          113           8
   117        7          112          10
   116        9          111           3

Thus, as expert testimony established, there is no statistical reason for setting the critical score at 116, and under normal classroom procedures the passing score would be lower. However, since there was a reasonable desire to limit the size of the register to the number needed to fill expected vacancies, normal classroom procedures were not controlling.
[4]  While "arbitrary" is defined either as based on individual judgment or discretion or as determined by whim or caprice, only the latter is prohibited in the exercise of administrative functions.
[5]  Proof, whether by direct or circumstantial evidence, is sufficient to constitute a preponderance when the proof, taken as a whole, shows that the fact or causation sought to be proved is more probable than not. Boudreaux v. American Ins. Co., 262 La. 721, 264 So.2d 621 (1972); Hanover Ins. Co. v. Jacobson-Young, Inc., 294 So.2d 564 (La.App. 4th Cir. 1974).
[6]  In attacking the critical score, plaintiffs also asserted that Belsom should have anticipated more vacancies because of a new retirement system. However, there was no evidence as to when the system was adopted or when the fact of more numerous vacancies became apparent. On October, 1976, 17 months after the critical score was set, Graffeo did inform Belsom that there were more vacancies then expected and requested more names to be added to the register. Belsom agreed to do so, but was informed such a procedure did not meet legal requirements. While we do not consider the legality, Belsom's willingness to add plaintiffs' names also militates against a finding of discrimination.
