Statistics Problem Solving Assignment 2: Compute The Followi ✓ Solved

Statistics Problem Solving Assignment 2compute The Following Proporti

Read each of the following questions carefully: calculate proportions, percentages, and rates based on the provided data. The data includes information on students' majors, gender, and other demographic variables. The tasks involve computing various proportions, percentages, ratios, and frequencies related to student majors and demographics. Additionally, construct frequency distributions, cumulative frequencies, and percentages based on survey data about film ratings and student satisfaction surveys. The assignment requires interpretation of data levels of measurement and calculation of ratios and percentages for different categories.

Sample Paper For Above instruction

Introduction

Statistical analysis provides valuable insights into demographic and survey data. In this paper, we analyze student data related to majors, gender, age, and satisfaction levels, and develop frequency distributions and ratios to understand patterns within the sample. Effective computation of proportions, percentages, and ratios unveils key trends and relationships, aiding in decision-making and policy formulation within educational and organizational contexts.

Analysis of Student Major and Gender Data

The provided data categorizes students according to their majors—Humanities, Social Sciences, Natural Sciences, Business, Nursing, Education—and gender—Male and Female. To analyze this data, we perform calculations including the proportion of specific groups within the total population, ratios between groups, and percentages to understand the distribution of students across various categories.

Firstly, the proportion of social science majors who are male is calculated as:

Proportion = Number of males in social sciences / Total number of social science students = 97 / (97 + 132) = 97 / 229 ≈ 0.423 or 42.3%

This indicates that approximately 42.3% of social science majors are male.

Secondly, the proportion of business majors who are female:

Proportion = Number of females in business / Total number of business majors = 35 / (3 + 35) = 35 / 38 ≈ 0.921 or 92.1%

This suggests that over 92% of business majors are female.

In the humanities, the ratio of males to females is:

Ratio = Number of males / Number of females = 117 / 83 ≈ 1.41:1

This ratio indicates that there are approximately 1.41 males for every female majoring in humanities.

The percentage of the total student body that are males is computed as:

Total students = sum of all students in each major category

Total students = (117 + 83) + (97 + 132) + (72 + 20) + (3 + 35) + (30 + 15) = 200 + 229 + 92 + 38 + 45 = 604

Total males = 117 + 97 + 72 + 3 + 30 = 319

Percentage of males = (319 / 604) × 100 ≈ 52.8%

This indicates that roughly 52.8% of the students are male.

The overall ratio of males to females is:

Total females = sum of all females = 83 + 132 + 20 + 35 + 15 = 285

Ratio of males to females = 319 / 285 ≈ 1.12:1

This means there are approximately 1.12 males for every female student.

Next, the proportion of nursing majors who are male is:

Number of males in nursing = 3

Total nursing students = 3 + 35 = 38

Proportion = 3 / 38 ≈ 0.079 or 7.9%

Regarding the percentage of the sample that are social science majors,

Total social sciences students = 97 + 132 = 229

Percentage = (229 / 604) × 100 ≈ 37.9%

Finally, the ratios between the different majors:

• Humanities to Business majors: 200 / 38 ≈ 5.26:1
• Female business to female nursing majors: 35 / 20 = 1.75:1

These ratios help compare the prevalence of majors within and across groups.

Frequency Distribution and Cumulative Percentages

Constructing a frequency distribution of survey responses on film ratings, where students rated the film on a 10-point scale, involves tallying the number of responses for each rating. For example, if the data observed indicates the ratings: 4, 2, 4, 2, 1, 3, 4, 3, 3, 3, 3, 3, 1, 3, 3, 2, 1, 3, 2, 4, then the frequency distribution would be:

• Rating 1: 3 responses
• Rating 2: 4 responses
• Rating 3: 7 responses
• Rating 4: 4 responses

Percentages are calculated by dividing each frequency by the total number of responses and multiplying by 100. Cumulative frequencies are summed sequentially to illustrate the accumulation of responses, aiding in understanding response distribution.

For the survey data assessing satisfaction with counseling services, frequencies and cumulative frequencies help identify the proportion of students satisfied, dissatisfied, or neutral, with organizations able to target improvements accordingly.

Constructing grouped frequency distributions involves categorizing data into intervals (e.g., age groups) and tallying responses within these ranges. Cumulative frequencies and percentages further enhance understanding by illustrating the accumulation of responses up to each interval.

Interpretation includes recognizing the level of measurement: nominal (e.g., satisfaction levels), ordinal (e.g., ratings), interval, or ratio. Most survey responses are ordinal or interval, allowing for meaningful calculations of central tendency and dispersion.

In conclusion, statistical analysis of survey and demographic data enables organizations and educational institutions to make informed decisions, tailor programs, and improve services based on empirical evidence.

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