Math Project 1 analysis Over the past twenty years, school tests in America have produced a general downward trend, whil

Math Project 1 analysis

Over the past twenty years, school tests in America have produced a general downward trend, while in the same period, the US has spent more on education than every country in the G20 group of large, developed economies. This report was written based on all inferential and cardinal data collected from the individuals who took the CAAP Critical Thinking Assessment in Seward County Community College from the year 2002 – 2011 using tables, graphs, and measures of centre to evaluate critical thinking assessment outcomes for Seward County Community College.

In this project on performance management for Seward County Community College and Area Technical School, we are analyzing data. The scores include all students offered the CAAP Critical Thinking Assessment at Seward County Community College in 2002-2011. On the spreadsheet should we look at the data on the spreadsheet, we can only guess or hypothesize about the data rather than analyzing the data as it is. This basic visual analysis was followed by the construction of a frequency distribution, which is a mathematical table aggregating the number of observations of each value a given variable can assume. When the frequency distribution of the test scores was made, it was noted that the distribution of data was negatively skewed. Skewed to the left means that the ‘mean’ of the data is much closer to the maximum value of the data, as was illustrated on the graph. We also know at a glance from the table that it is skewed to the left because if I were to draw a line of estimation for the data, the much longer ‘tail’ represents a statistic ‘skewed to the left’ sign.

The graph and frequency table demonstrate to us that the mean of the data is 61-70 because most of the frequencies are in this interval and also that there is an outlier, which is a value that is apart from other values in the 0-10 score interval. The next step we took to analyze this data was to take the mean score from each year and provide a time series that depicts trends in the data. There is, in fact, very little point-to-point variation in the graph given below. Speaking of the score data of 2002-2011, they didn’t let the output go below an average of 60 scores per year. The highest level of average score change was observed in 2008 at the level of 60.16.

We then computed the mean, median and standard deviation of the data so as to get more information regarding the scores. There was a mean successful pass rate of 59.67, a median of 60 and a standard deviation of 5.29. The mean is all the scores we have from 2002-2011, where the scores were added together for the total score and then divided by the number of scores; then, for the nine years, the average score from the overall scores was 59.7. This is the average of the data if all of the scores are arranged in the order of magnitude and the two middle numbers are added and divided by two. The standard deviation is a term used to explain how much your measurements of a particular group deviate from the average, commonly called the ‘Expected value’. If a standard deviation is low, it means that most of the numbers are also very close to the given average. A high standard deviation indicates that the number is distributed far apart. Our standard deviation is 5.29, which tells me that most of the numbers are extremely close to the average. The frequency and time series graph above can also confirm this.

Population Summary Parameter:

Table 2 below presents summary statistics of the data, including the means, medians and standard deviations of a random sample of the data. Not surprisingly, the mean and median of the given sample differ insignificantly from the mean and median parameters of the population data. In the same way, the sample standard deviation is a statistic estimator of the population standard deviation because the sample standard deviation is not near the value of the population standard deviation.

Random Sample Summary Statistics:

A few techniques were followed to obtain a random sample for the calculation of summary statistics used to compare with the summary parameters of a population. Using the Excel program, the random sample was developed. The first approach was adopted with regard to the test scores by sorting them into different tables depending on the year of the test score. Secondly, to make them more realistic, the random function in Excel was applied to assign a random number to every score in all the given tables. Thirdly, the values in the random number column were arranged in ascending order in each table. Lastly, from each year, the ten top participants are chosen to be in the sample. Altogether, 870 test scores were taken at random, while each chosen year had 10 test scores that were chosen randomly.

As shown above, the five-number summary of the population was used to construct the box plot. A boxplot is a graph that contains a line joining the least value and the largest value and a block containing vertical lines in the middle of the block at the first quartile Q1, the median or second quartile Q2, and the third quartile Q3. Since the five-number summary is identified above, then the values are as follows: minimum being 0, Q1 is 56 while Q2 or median is 69, Q3 is 64, and the maximum is 73. This means that, at least on average, 25% of the arranged test marks are 56 or lower, and at least on average, 75% of the marks are 56 or higher. It goes on to note that the median during the second quarter was 60, which is the same figure. It splits the test scores by ranking them in ascending order and then preserving only the last 50% of ranks. Further, Q3 = 64 has the meaning that not less than 75% of the values lying after the arrangement are ≤ 64 and not less than 25% of the values are ≥ 64. It is also evident from the box plot that the population data has a skewed distribution with an outlier at 0, which makes the curves skewed to the left.

COLUMN

Min

Q1

Median

Q3

Max

t-score

0

56

60

64

73

Thus, different from national test scores displayed for 2002 – 2011, the histogram, boxplot, and summary statistics demonstrate that the results of the Critical Thinking Assessment for Students of Seward County Community College have remained unchanged over this period. While all four histograms, box plots and summary statistics showed that the test scores are low, I found that the community college practices are not typical for the whole nation. In the next report, it will be possible to consider factors that are supporting the stable trend.