Question 1: True or False
Indicate whether each of the following statements is true or false:
a. Statistics is the science of collecting, organizing, analyzing, interpreting, and presenting data.
b. A statistic is a single measure, reported as a number, used to summarize a sample data set.
c. Descriptive statistics refers to generalizing from a sample to a population, estimating unknown parameters, drawing conclusions, and making decisions.
d. One of the advantages of censuses is that they provide up-to-date data.
e. Inferential statistics refers to the collection, organization, presentation, and summary of data, either by using charts and graphs or through numerical summaries.
Question 2: Data Analysis
The following are the final scores in Probability and Statistics for 40 selected Year 1 Computer Science students during the academic year 2023:
30, 83, 90, 83, 75, 45, 90, 90, 68, 83, 58, 83, 73, 78, 90, 83, 53, 70, 55, 35,
31, 45, 64, 73, 65, 45, 80, 80, 68, 73, 48, 73, 73, 78, 80, 63, 43, 60, 45, 55.
(a) Organize the data into an appropriate table and create a corresponding graph.
(b) Identify the mode of the data set.
(c) Compute the following summary measures:
Arithmetic mean
Median
Variance
Standard deviation
The correct answer and explanation is:
Explanation
Statistics plays a crucial role in analyzing and interpreting data effectively. In the given dataset, we have scores from 40 Year 1 Computer Science students in Probability and Statistics. Our goal is to organize this data, visualize it, and compute key statistical measures.
(a) Data Organization and Visualization:
The dataset was organized into a frequency table, displaying the number of times each score appears. A histogram was also generated to provide a visual representation of the frequency distribution. This histogram helps in identifying patterns, such as whether the data is skewed or symmetric.
(b) Identifying the Mode:
The mode represents the most frequently occurring value in the dataset. From the frequency table, we found that 73 is the mode, meaning it appears the most times among students’ scores.
(c) Summary Measures Computation:
- Arithmetic Mean: The mean is the average score, calculated as the sum of all values divided by the total number of observations. The computed mean is 66.43, indicating that the typical score hovers around this value.
- Median: The median is the middle value when the data is ordered. With 40 values, the median is the average of the 20th and 21st values, which results in 71.5.
- Variance: This measure reflects the spread of scores from the mean. The variance calculated is 297.23, indicating how much the scores deviate from the mean.
- Standard Deviation: The square root of variance gives the standard deviation, which is 17.24. This suggests that most scores deviate around ±17.24 points from the mean.
In conclusion, these statistical measures help in understanding the overall performance of students. The high variance and standard deviation indicate considerable variation among students’ scores. A higher mode suggests that many students scored around 73, making it the most common score in the dataset.