Introduction

Is there a difference in SAT scores when looking at gender? Some say that males do better on the math section and females outscore males on the verbal section. These perceptions may be so ingrained in our society that girls choose humanities-based majors while males fill STEM- based majors. These perceived gender discrepancies may be altering pivotal life choices. What follows is an analysis of SAT in an effort to see if there is indeed a gender difference in performance on the SAT.

The Data

303 observations were collected from NorCal High. The varaibles collected were gender, verbal SAT score, and math SAT score. There were 158 males and 145 females in the study.

What is the total performance of the group?
totalsat= sat$math + sat$vrbl
summary(totalsat)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    650    1105    1230    1207    1330    1550 
hist(totalsat, col="light blue")

In general, the average scores are between 1100 and 1400. The data is skewed to the left and unimodal. The average score is about 1100. The lowest score is around 600 and the stop score is 1600. The range is 1000 points.

How did each gender do?
satfemale <- subset (sat, sat$gndr == "1")
satmale <- subset (sat, sat$gndr == "0")
maletotal= satmale$math + satmale$vrbl
femaletotal=satfemale$math +satfemale$vrbl
summary(femaletotal)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    750    1090    1210    1186    1320    1520 
summary(maletotal)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    650    1110    1255    1226    1350    1550 
boxplot(femaletotal, maletotal, xlab="Female--Male", ylab="SAT Score", main="SAT Scores and Gender")

In general, the average female score is 1210, and the average male score is 1255. Both data sets are relatively skewed left. The females high score is 1520 and the lowest score is 750. The males highest score is 1550, and the lowest score is 650 but it is an outlier.

mathscore <- (sat$math)
vrblscore <- (sat$vrbl)
gender <- (sat$gndr)
femalemath <- (satfemale$math)
malemath <- (satmale$math)
femalevrbl <- (satfemale$vrbl)
malevrbl <- (satmale$vrbl)
Is there a difference in math score in terms of gender?
summary(malemath)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    290     570     640     629     690     800 
summary(femalemath)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  360.0   530.0   600.0   592.1   660.0   800.0 
boxplot(malemath, femalemath, ylab="Math SAT Score", xlab="Male--Female", main="Math Scores by Gender")

In general, male score higher on the math section of the SAT. Both have a maximum score of 800. The lowest female score is 360, and the lowest male score in 290, though it is an outlier. The average score for males is 640, and the average score for females is 600. The boxplots are both relatively skewed to the left.

summary(femalevrbl)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  280.0   530.0   610.0   594.1   660.0   770.0 
summary(malevrbl)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  310.0   540.0   600.0   596.6   667.5   800.0 
boxplot(malevrbl, femalevrbl, xlab="Male--Female", ylab="SAT Verbal Scores", main= "Verbal Scores by Gender")

While females have a higher median (610) compared to males (600). The male subgroup is higher on all other summary statistics, including both the minimum and maximum.The females have a low score of 280 and the males lowest score is 310. The Males boxplot is relatively symetric, and the female graph is relatively skewed to the left

Conclusion While the distributions seem to indicate that males from NorCal high are performing better than females, more tests would need to be performed to show whether or not it is a statistically significant difference. This is a large sample size (n = 303) but performance on the SAT may vary from year to year. In addition, we can only generalize our findings to this high school, because the sample was specific to NorCal High. A better approach to answer this question may be to take a random sample of SAT data from nationwide results. It may be beneficial to collect information regarding other variables, in addition to gender, verbal and math scores. Some other variables to consider may be gpa (quantitative), number of AP/Honors courses taken (quantitative),race/ethnicity (categorical), highest math course taken (categorical), socioeconomic status based on parent income (categorical), and the region of the United States in which the student lives (categorical). This would allow us to expand our research beyond gender as there are many other factors that affect SAT performance.

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UC9Ib25vcnMgY291cnNlcyB0YWtlbiAocXVhbnRpdGF0aXZlKSxyYWNlL2V0aG5pY2l0eQooY2F0ZWdvcmljYWwpLCBoaWdoZXN0IG1hdGggY291cnNlIHRha2VuIChjYXRlZ29yaWNhbCksIHNvY2lvZWNvbm9taWMgc3RhdHVzIGJhc2VkIG9uCnBhcmVudCBpbmNvbWUgKGNhdGVnb3JpY2FsKSwgYW5kIHRoZSByZWdpb24gb2YgdGhlIFVuaXRlZCBTdGF0ZXMgaW4gd2hpY2ggdGhlIHN0dWRlbnQgbGl2ZXMKKGNhdGVnb3JpY2FsKS4gVGhpcyB3b3VsZCBhbGxvdyB1cyB0byBleHBhbmQgb3VyIHJlc2VhcmNoIGJleW9uZCBnZW5kZXIgYXMgdGhlcmUgYXJlCm1hbnkgb3RoZXIgZmFjdG9ycyB0aGF0IGFmZmVjdCBTQVQgcGVyZm9ybWFuY2UuCg==