My representative sample consists of the test results that were collected in a M

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My representative sample consists of the test results that were collected in a Mathematics class with a total enrollment of twenty students and a test that was composed of twenty different multiple-choice questions (“The Statistics of Classroom Assessment,” 2018). The data set contains a series of numbers, each of which corresponds to a score that a student has achieved (with a total possible earned point of 20).
Below is the data set;
{20,17,16,14,14,12,12,12,10,10,10,10,10,8,8,8,6,6,4,3} {20,17,16,14,14,12,12,12,10,10,10,10,10,8,8,8,6,6,4,3}
The information is intriguing to look at because it represents the test scores that each student in the class achieved while taking the mathematics exam. Through the examination of the data set’s measured central tendencies and variance, a thorough analysis can be performed with little effort.
The Mean Value
The mean is the average of the test scores of all twenty students in the population (Manikandan, 2011). The mean is determined by taking the total number of possible points, 210, and dividing that by the total number of students who took the exam (20), which yields a value of 10.5. Therefore, the average score that is the mean is 10.5 Marks.
Median Value
The test score that is deemed to be near the midpoint of the scattered results is the one that is believed to be the median. Finding the median requires arranging the data set either from least to greatest or greatest to least before doing the calculation. Due to the fact that there are an even number of test scores in the dataset, the scores that are considered to be in the middle are both 10. As a result, the mean between the two test scores is determined in order to find the median, which is accomplished by adding the two test scores (10+10=20) and dividing by (2), which is 10, in order to arrive at the value of 10.
Modal Value
It is the most common test score that appears in the data collection of test scores. According to the data, five pupils achieved a score of 10 in the exam. In this case, it’s a mode of 10.
Range
The data set’s range informs us how wide the test results are spaced out. In order to arrive to this result, we must subtract the highest and lowest values from the entire set of results. The highest score is 20 while the lowest score is 3 thus to get the range, we find out the difference between the two values which is 20-3=17.
Standard Deviation
The standard deviation is a statistical measure that illustrates the degree to which the distribution of the test results (obtained from a sample of 20 students) deviates from the mean of the data set (Hargrave, 2019). The following is the formula for calculating a population’s standard deviation:
Where ‘n’ represents the total number of students who participated in the exam and ‘xi’ represents the individual student’s score on the exam. First, we take the summation of the squared sum of the difference between each test score and the mean, and then we divide that by the total number of students in the population to get the numerator. The final step in calculating the standard deviation is to take the square root of the entire value. The calculation for the standard deviation is presented in the following example:
Therefore, 4.201 is the value of the standard deviation.
References
Hargrave, M. (2019). Standard deviation definition. Retrieved May, 13, 2019.
Manikandan, S. (2011). Measures of central tendency: The mean. Journal of Pharmacology and Pharmacotherapeutics, 2(2), 140.
good overall job here.
Can you elaborate on how you calculated the standard deviation? This is probably “the” most important calculation in statistics. I suggest using technology, like my stats_calculator. (I posted my stats_calculator near the beginning of the Week 1 discussion.)
NOTE: We should calculate the SAMPLE standard deviation instead of the population standard deviation. The 20 students here are a sample of the overall population of students.
Were you able to duplicate your calculations using my stats_calculator?
My stats_calculator is an Excel file, with already formatted “templates” where you can quickly analyze complex situations. Be sure to use technology, like my stats_calculator, as much as possible. I posted this, along with the link to my videos, near the beginning of this week’s graded discussion area. I created my stats_calculator to eliminate most of the “arithmetic” so we could focus on the actual applications.
We will use technology for everything. Doing the calculations manually, using formula, simply takes far too long. It might be OK to do one or two questions “by hand” just to get a feel for the underlying arithmetic. After enjoying that, however, we want to use the fastest methods available, like my stats_calculator.

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