Descriptive Measures and Graphical Representation of Student Test Score Distributions
Overview
This assignment analyzes student test score datasets using descriptive statistics and graphical methods. It calculates measures of central tendency, spread, and position (mean, median, mode, range, quartiles, percentiles, variance, and standard deviation) for one dataset, then applies graphical representations (stem-and-leaf plot, histogram, and box plot) to a second dataset to identify outliers and distribution patterns.
What this coursework covers
- Descriptive Measures of Student Test Scores: calculation of range, quartiles, percentiles, mean, median, mode, variance, and standard deviation for a 9-value dataset
- Comparison and Explanation: relationship between quartiles and percentiles with theoretical justification
- Graphical Representation: stem-and-leaf plot, histogram, and box plot analysis of 25-value dataset with outlier identification
Preview
Assignment Activity Unit 2
Donald Ngonyo
University of the People
MATH 1280 - Introduction to Statistics
Nikhil Choksi
April 23, 2026
Assignment Activity Unit 2
Question 1: Descriptive Measures of Student Test Scores
45 | 62 | 75 | 85 | 90 | 93 | 95 | 95 | 100 |
The data is arranged in ascending order, which makes it easier to determine location and spread measures.
Range
The range measures the spread between the highest and lowest values in the dataset. To calculate it in Excel or LibreOffice Calc, identify the maximum score using =MAX (range) and the minimum score using =MIN(range), then subtract the minimum from the maximum (Illowsky et al., 2023).
Highest score = 100
Lowest score = 45
Range = 100 – 45 = 55
This means the scores are spread across 55 points, indicating moderate variability.
Quartiles and Percentiles
Quartiles divide the dataset into four equal parts, while percentiles divide it into 100 equal parts. According to OpenStax, the first quartile corresponds to the 25th percentile and the median correspond to the 50th percentile (Illowsky et al., 2023).
Working Process
Number of values = 9
Median position = (9+1)/2 = 5th value = 90
Lower half: 45, 62, 75, 85
Upper half: 93, 95, 95, 100
Q1 = average of 62 and 75 = 68.5
Q3 = average of 95 and 95 = 95
Therefore:
- Q1 = 68.5
- Q3 = 95
- 25th percentile = 68.5
- 50th percentile = 90
Mean, Median, Mode, Variance, Standard Deviation
Mean
Sum = 840
Number of values = 9
Mean = 840 / 9 = 82.22
Median
In Excel use =MEDIAN (range)
Middle value = 90
Mode
In Excel use =MODE (range)
Most frequent score = 95
Variance
In Excel use =VAR.S(range) for sample variance
Variance = 334.19
Standard Deviation
In Excel use =STDEV.