UNIT 2: Written Assignment

HS 4241 - 01 Psychopathology and Mental Health - UNIT 2 Written Assignment Instructor: Pankaj Mehrotra Date: 09/02/2025 QUESTION 1 The mean pulse rate is determined for each of the following age groups, which are created at 5-year intervals: 10–14, 15–19, 20–24, 25–29, etc. Due to one fractional age (11.5 years) and three missing gender values, the total number of participants used for calculations was 22 rather than 25. Since there was only one participant for some ages, their pulse rate is the same as the category mean. There were 22 participants in all (not including missing gender values). Males (M): 10 individuals There were nine female contestants (F). Three participants (not included in proportion estimates) have missing genders. Male Proportion = 10/19 × 100 = 52.6% The percentage of females is 9/19 × 100 = 47.4% QUESTION 2 The best way to show the average pulse rate across age groups is with a bar chart. The mean pulse rate would be on the y-axis, and each age group (e.g., 10–14, 15–19, etc.) would be displayed on the x-axis. Each bar's height would represent the category's average pulse rate. Why Use a Bar Chart? Comparisons between various age groups are evident.aids in spotting patterns, such as the age-related variations in pulse rate.Even for audiences who are not statisticians, it is simple to understand. The percentage of males and females in the sample can be shown with a pie chart. There would be two parts on the chart: one for men (52.6%) and one for women (47.4%). Why use a pie chart? It effectively conveys relative proportions in an understandable visual manner. Helps draw attention to the study's gender distribution. It is easy to use and well-known for categorical data. Each age group's pulse rate distribution may be depicted using a boxplot if we preferred to display individual pulse rates rather than means. QUESTION 3 Step 1: Calculate the Arithmetic Mean (Average) Pulse Rate For Males: Mean = 979+90+75+60+65+79+54+98+49​= 649 / 9 = 72.11 bpm For Females: Mean = 966+59+79+95+72+55+64+60+65​= 615/9 = 68.33 For Both Genders Together: Mean = 18649+615​= 1264 / 18​= 70.22bpm Step 2: Calculate the Median For Males (Sorted List: 49, 54, 60, 65, 75, 79, 79, 90, 98) ●​ Median is the middle value (5th value in the sorted list): 75 bpm For Females (Sorted List: 55, 59, 60, 64, 65, 66, 72, 79, 95) ●​ Median is the middle value (5th value in the sorted list): 65 bpm For Both Genders Together (Sorted List: 49, 54, 55, 59, 60, 60, 64, 65, 65, 66, 72, 75, 79, 79, 79, 90, 95, 98) ●​ Median is the middle value (9th and 10th values): 65+66 / 2=65.5 bpm Step 3: Degrees of Freedom (df) df = n - 1 For Males: df = 9 - 1 = 8 For Females: df = 9 - 1 = 8 For Both Genders Together: df = 18 - 1 = 17 Step 4: Calculate the Standard Deviation (s) For Males: 16.40bpm For Females: 12.29bpm The standard deviation of male pulse rates (16.40 bpm) is higher than that of females (12.29 bpm), suggesting that male pulse rates are more variable. This implies that whereas female pulse rates are more constant, males in the study have more extreme values (such as 98 and 49 bpm). Step 5: Calculate the Range and Interquartile Range (IQR) for Both Genders Together Range: Range= Max − Min = 98 − 49 = 49bpm Interquartile Range (IQR): 1st Quartile (Q1) = Median of first half of data (55, 59, 60, 60, 64, 65, 65, 66, 72) ●​ Q1 = 60 3rd Quartile (Q3) = Median of second half of data (72, 75, 79, 79, 79, 90, 95, 98) ●​ Q3 = 79 IQR = Q3 - Q1 = 79 - 60 = 19 QUESTION 4 Step 1: Calculate the Mean Length of Stay for ‘Intensive Care Unit’ and ‘Surgery’ Together The formula for the weighted mean is: where: ●​ ni​= number of beds in each department ●​ Xi​= mean length of stay for each department For Intensive Care Unit (ICU) and Surgery: Xˉ= (260+240) / 30​= 500 / 30 =16.67 days So, the mean length of stay for ICU and Surgery together is 16.67 days. Step 2: Calculate the Mean Length of Stay for All 4 Departments Together Xˉ= (260+240+160+400) / 120 ​= 1060 /120 = 8.83 days So, the mean length of stay across all four departments is 8.83 days. REFERENCES: ●​ Illowsky, B. and Dean, S. (2017). Introductory Statistics. OpenStax Rice University. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0). Retrieved from https://my.uopeople.edu/pluginfile.php/1954716/mod_page/content/3/TEXT%20intro ductory-statistics.compressed.pdf