Daniel BraconnierH PreCalc.Mrs. Ellis4/30/2012

Statistical Analysis of SAT Scores

In this statistical analysis of SAT scores, the raw data was applied in many ways. With the help of autograph a dot plot, stem and leaf diagram, histogram, and box plot were created. From the raw data and graphs a list of calculated statistics were calculated. All graphs and statistics were interpreted and analyzed.

Dot Plot:

400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 7000

1

2

3

4

x

f

This dot plot shows the number of states that have received an average SAT score over which the dots are.

Stem and Leaf Diagram for Raw Data:0: 100:200:300:400: 75 78 82 82 93 95 97 98 98 99 99 99500: 2 3 6 7 9 10 11 12 13 13 14 14 17 18 25 25 26 40 40 42 46 47 48 51 53 55 56 58 60 65 68 68 71 72 76 85 88 95 98 98 98600: 5700:

Average SAT Sc

Histogram:

300 400 500 600 700 8000

10

20

30

40

50

x

f

This histogram showed the amount of states with an SAT score average in the intervals 400-500, 500-600,600-700.

Box Plot:

400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 70010

20

30

x

f

This box plot showed many of the statistics listed below. Statistics:Mean: 529.1Median: 525Mode: 499Range: 130Inter-quartile Range: 65Five Number Summary: 475, 500, 525, 565, 605Outliers: 475 and 605Variance: 1992Standard Deviation: 44.64

Average SAT Sc

Average SAT Sc

Interpretation:The dot plot showed the number of states that have received an average SAT score over

which the dots are. This also showed which scores are the most common and or least received SAT score average. The stem and leaf diagram displayed the raw data in a more organized and condensed way from least to greatest SAT score average. The histogram showed the amount of states with an SAT score average in the intervals 400-500, 500-600,600-700. The box plot displayed the median and the four quartiles. From the box plot the inter-quartile range and five number summary were calculated and or displayed. There was a trend that most of the state’s average SAT scores were in the 500s; very few states averaged in the 600s and only a handful averaged in the 400s. There were some unusual features to the data; the two outliers of the data set were an average SAT score of 475 from South Carolina and an average SAT score of 605 from North Dakota.

Scatter Plot:

0 45 90400

420

440

460

480

500

520

540

560

580

600

620

640

660

680

700

x

y

Mean (, ): (37, 533.5)

r=-0.8824

This scatter plot showed the relation between the rate and or percentage of the amount of people in each state who take the SATs and the average SAT scores received.

The coefficient of determination “r” was -0.8824, this exemplifies that the regression line was not too good in the way it correlated with the data in the scatter plot. A more reliable coefficient would be one closer to -1 and or 1.

The slope of the regression line was a negative slope; which means as the X in the this case the % rate went up the Y in this case the average SAT score went down. This inverse relationship between X and Y shows that as % rate went up Sat scores went down.

Because the correlation coefficient of the data was negative it affected the best fit line’s slope; causing it to be negative as well. Thus the inverse relation interpreted from the scatter plot can be easily interpreted from the best fit line’s inverse slope.

The coefficient of determination of the data was significant to the best fit line because it verifies how well the line fits with the data in the scatter plot. The number was -0.8824; this is

Ave

rage

SA

T

Sco

res

% Rate

pretty close to a perfectly matching coefficient of -1. Thus the best fit line is a good representation of the trend occurring in the scatter plot.

Two Paragraphs:From this statistical analysis one can infer that the relationship between the % rate and

Average SAT score is inverse and a bit odd. One would think that given the chances if more kids, from the states with the higher % rate, are taking the SATs then the average SAT score should be high. This ideology is the one that seem most probable, because one would think as the opportunity for kids to take the SATs grew higher in, from the states with the higher % rate, the kids would be better educated and thus the state would have a higher average SAT score.

However, this is not the case. Clearly as % rate goes up average SAT scores go down. This is highly realistic for as more people take the SATs in one state, the probability of receiving a higher average SAT score shrinks with the growing probability of a kid to do poorly on the SATs. On the other hand, the states with the smallest % rate seem to be getting the highest scores. Although this is the case based on the inverse relation, most likely that state has students take the ACTs more often than the SATs. Thus the only kids who actually end up taking the SATs from such a state are going to do well on them; for this kid most likely is only taking the SATs to get into a better college that would rather look at SAT scores than ACT scores.