Week 7 GEC Math BSN PDF

Mathematics in the Modern World Instructor: Prince Steven Arvie C. Vitug, RME WEEK 7 : PRETEST WEEK 7 : PRETEST (Recitation) 1. Imagine you and your friends all got different scores on a test. If everyone's scores are very close to each other? What does it mean? Is there a little dispersion or a lot of dispersion? If everyone's scores are very close to each other? What does it mean? If everyone's scores are very close to each other, there's little dispersion. If the scores are very different from each other, there's a lot of dispersion. WEEK 7 : PRETEST (Recitation) 2. What is measures of dispersion for? WEEK 7 : PRETEST (Recitation) 2. What is measures of dispersion for? Dispersion helps you understand whether the scores or values are closely packed together or widely spread apart. Measures of Dispersion In addition to locating the center of the given data points of the quantitative variable, another important aspect of describing the variable is determining the extent of variation of the data point. This could be done geometrically, that is describing the spread of the data points by looking the corresponding dot plot of the data set or by computing the numerical measures of spread of the data points. These measures are referred to as measures of dispersion (variability). Some of the most frequently used measures of dispersion are the range, the interquartile range, the variance and the standard deviation. Similar to the measures of centrality, there are sample measures and population measure of dispersion. These sample measures of dispersion are used to estimate the population measures which are usually unknown. How do we compute for the measures of dispersion? The Range The Range, denoted by R, is the simplest measure of dispersion and is usually used to describe the spread of data points in a small data set. It is deﬁned as the shortest distance of two points that contain all the given data. Thus, it is obtained by computing the difference between the largest and the smallest observed value of the variable in the data set. Example Let's say a nurse measures the blood pressure of 5 patients and records their systolic blood pressure as follows: 110, 130, 125, 140, 115 Maximum Value: 140 Minimum Value: 110 Range = 140 − 110 = 30 The Interquartile Range Interquartile range, denoted as IQR, is a measure of dispersion of where “middle ﬁfty (50%)” of the data set is located. It can be computed by getting the difference of the third quartile (Q3) and ﬁrst quartile (Q1) values, that is: Example ( if the data set is odd ) 1. Now, let’s take the pulse rates (in beats per minute) of 7 patients: 65, 60, 75, 80, 72, 68, 70 Step 1: Order the data (ascending) 60, 65, 68, 70, 72, 75, 80 Step 2: Find the median Median = 70 Example Step 1: Order the data (ascending) 60, 65, 68, 70, 72, 75, 80 Step 4: Find the IQR Step 2: Find the median Median = 70 IQR = Q3 - Q1 IQR = 75 - 65 Step 3: Split into two halves: IQR = 10 (lower set) Q2 (upper set) Q1 = 65 ( 60, 65, 68 ) 70 ( 72, 75, 80 ) Q2 = 70 Q1 Q3 Q3 = 75 Example ( if the data set is even ) 2. Let’s say a nurse records the recovery times (in hours) of 8 patients after surgery: 9, 7, 5, 10, 12, 18, 16, 14 Step 1: Order the data (ascending) 5, 7, 9, 10, 12, 14, 16, 18 Step 3: Find the IQR Step 2: Split into two halves: IQR = Q3 - Q1 (lower set) (upper set) IQR = 15 - 8 IQR = 7 (5, 7, 9, 10) (12, 14, 16, 18) Q1 = 8 Q3 = 15 Q1 Q3 Let’s solve faster! Calculate the Range: 1. 120, 135, 140, 125, 130 4.) 70, 85, 78, 90, 82 2. 98.6, 99.2, 97.8, 98.4, 100.0 5. ) 85, 92, 88, 96, 91 3. 45, 55, 50, 60, 48 Calculate the Interquartile Range: 1. 14, 22, 25, 30, 33, 37, 40 2. 5, 7, 8, 12, 15, 18, 21, 24, 28 3. 10, 15, 19, 22, 27, 32, 35 4. 16, 18, 22, 25, 28, 30, 32, 35 5. 45, 50, 52, 55, 60, 62, 65, 70 The Variance Variance measures how much the data points in a set deviate from the mean, giving an idea of the spread or dispersion in the data. It is the average of the squared differences between each data point and the mean. The Standard Deviation The standard deviation is the commonly used measure of dispersion. It is the square root of the variance and often described as the average distance of the data points in the data set around its mean. Population Standard Deviation Sample Standard Deviation or simply , or simply , Example 1. Find the Standard Patient Systolic BP (mmHg) xi Deviation. Suppose a nurse measures the systolic 1 120 blood pressure (in mmHg) 2 130 of 5 patients as follows: 3 110 120, 130, 110, 140, 125 4 140 5 125 Step 1: Find the mean(x̄) Example Step 2: Create a Table for Squared Differences: We will calculate the difference of each value from the mean, square the differences, and then sum them up. note : from the Patient xi xi - x̄ (xi - x̄)2 previous step, mean x̄ = 125 1 120 120 - 125 = -5 (-5)2 = 25 2 130 130 - 125 = 5 52 = 25 3 110 110 - 125 = -15 (-15)2 = 225 add 4 140 140 - 125 = 15 152 = 225 5 125 125 - 125 = 0 02 = 0 Example Note: from the previous step, Step 3: Calculate the Sample Variance (s²): Step 4: Calculate the Standard Deviation (s): Let’s solve faster! Calculate the Variance and Standard Deviation: 1. 5, 7, 8, 10, 12 2. 12, 15, 20, 25, 30 3. 22, 25, 27, 30, 35 WEEK 7 : SEATWORK 1 Week 7 : Seatwork 1 Instructions: Write the letter of the correct answer. 1. Which of the following is a measure of dispersion that indicates the spread of data around the mean? A) Mean B) Median C) Variance D) Mode Week 7 : Seatwork 1 Instructions: Write the letter of the correct answer. 2. What is the name of the measure of dispersion that is calculated as the square root of the variance? A) Range B) Standard Deviation C) Interquartile Range D) Mean Absolute Deviation Week 7 : Seatwork 1 Instructions: Write the letter of the correct answer. 3. Which measure of dispersion is describe the spread of data points in a small data set? A) Range B) Standard Deviation C) Interquartile Range D) Mean Absolute Deviation Week 7 : Seatwork 1 Instructions: Write the letter of the correct answer. 4. Which measure of dispersion is best used to understand the variability of the middle 50% of the data? A) Variance B) Standard Deviation C) Range D) Interquartile Range Week 7 : Seatwork 1 Instructions: Write the letter of the correct answer. 5. If the variance of a dataset is 64, what is the standard deviation? A) 64 B) 8 C) 16 D) 32 Week 7 : Seatwork 1 Instructions: Write the letter of the correct answer. 6. For a dataset with a mean of 15 and standard deviation of 4, what is the variance? A) 64 B) 8 C) 16 D) 32 Week 7 : Seatwork 1 Instructions: Write the letter of the correct answer. 7. A dataset has the following values: 6, 8, 10, 14, and 20. What is the interquartile range (IQR)? A) 6 B) 8 C) 10 D) 12 Week 7 : Seatwork 1 Instructions: Write the letter of the correct answer. 8. A dataset has the following values: 3, 6, 6, 9, 12. What is the range? A) 9 B) 8 C) 6 D) 10 Week 7 : Seatwork 1 Instructions: Write the letter of the correct answer. 9. If a dataset has values 11, 13, 15, 17, and 19, what is the standard deviation? A) 2.7 B) 2.4 C) 2.0 D) 3.0 Week 7 : Seatwork 1 Instructions: Write the letter of the correct answer. 10. A dataset contains the following values: 7, 15, 23, 31, 39. Calculate the variance. A) 140 B) 160 C) 180 D) 200 Exchange papers “I AM AN HONEST AND RESPONSIBLE NURSING STUDENT.” Week 7 : Seatwork 1 Instructions: Write the letter of the correct answer. 1. Which of the following is a measure of dispersion that indicates the spread of data around the mean? A) Mean B) Median C) Variance D) Mode Week 7 : Seatwork 1 Instructions: Write the letter of the correct answer. 2. What is the name of the measure of dispersion that is calculated as the square root of the variance? A) Range B) Standard Deviation C) Interquartile Range D) Mean Absolute Deviation Week 7 : Seatwork 1 Instructions: Write the letter of the correct answer. 3. Which measure of dispersion is describe the spread of data points in a small data set? A) Range B) Standard Deviation C) Interquartile Range D) Mean Absolute Deviation Week 7 : Seatwork 1 Instructions: Write the letter of the correct answer. 4. Which measure of dispersion is best used to understand the variability of the middle 50% of the data? A) Variance B) Standard Deviation C) Range D) Interquartile Range Week 7 : Seatwork 1 Instructions: Write the letter of the correct answer. 5. If the variance of a dataset is 64, what is the standard deviation? A) 64 B) 8 C) 16 D) 32 Week 7 : Seatwork 1 Instructions: Write the letter of the correct answer. 6. For a dataset with a mean of 15 and standard deviation of 4, what is the variance? A) 64 B) 8 C) 16 D) 32 Week 7 : Seatwork 1 Instructions: Write the letter of the correct answer. 7. A dataset has the following values: 6, 8, 10, 14, and 20. What is the interquartile range (IQR)? A) 6 B) 8 C) 10 D) 12 Week 7 : Seatwork 1 Instructions: Write the letter of the correct answer. 8. A dataset has the following values: 3, 6, 6, 9, 12. What is the range? A) 9 B) 8 C) 6 D) 10 Week 7 : Seatwork 1 Instructions: Write the letter of the correct answer. 9. If a dataset has values 11, 13, 15, 17, and 19, what is the standard deviation? A) 2.7 B) 2.4 C) 2.0 D) 3.0 Week 7 : Seatwork 1 Instructions: Write the letter of the correct answer. 10. A dataset contains the following values: 7, 15, 23, 31, 39. Calculate the variance. A) 140 B) 160 C) 180 D) 200 Linear Correlation In data analysis, the linear relationship (association) of two quantitative variable is called as linear correlation. There are two types of linear relationship: 1. The positive (also knowns as direct relationship) - if y increases as x increases 2. The negative relationship (also known as indirect or inverse relationship). - if y decreases as x increases Coefficient of Correlation The coefﬁcient of correlation (often represented by 𝑟) is a statistical measure that quantiﬁes the strength and direction of the relationship between two variables. It is also known as Pearson's correlation coefﬁcient when using linear relationships. The value of 𝑟 ranges from -1 to +1. The Pearson’s Correlation is formulated as follows: The value of r and the Corresponding Strength of Linear Relationship Note: The value of 𝑟 ranges from -1 to +1. Strength of the Linear Relationship Coefficient 𝑟 Very Weak or No Relationship -0.09 to 0.09 Weak Relationship 0.10 to 0.30 -0.10. to -0.30 Moderate Relationship 0.31 to 0.50 -0.31 to -0.50 Strong Relationship 0.51 to 1.00 -0.51 to -1.00 The value of r and the Corresponding Strength of Linear Relationship Example 1. The goal is to determine the correlation between a patient's height (in cm) and their weight (in kg) using Pearson's correlation coefﬁcient. Patient Height 𝑥 (cm) Weight 𝑦 (kg) 𝑥2 𝑦2 𝑥𝑦 1 165 72 27225 5184 11880 2 150 60 22500 3600 9000 3 175 68 30625 4624 11900 4 160 75 25600 5625 12000 5 170 65 28900 4225 11050 Example Step 1: Summing the values: Step 2: Apply Pearson's Correlation Formula: Based on the table what is the strength of Linear Relationship? Strength of the Linear Relationship Coefficient 𝑟 Very Weak or No Relationship -0.9 to 0.09 Weak Relationship 0.10 to 0.30 -0.10. to -0.30 Moderate Relationship 0.31 to 0.50 -0.31 to -0.50 Strong Relationship 0.51 to 1.00 -0.51 to -1.00 Interpretation The correlation coefﬁcient 𝑟 = 0.31 suggests a moderate positive correlation between height and weight. This implies that there is a noticeable positive relationship between a patient's height and weight. As a patient's height increases, their weight tends to increase as well, though the relationship is not perfect or strong. In a nursing context, understanding a moderate positive correlation between height and weight can assist in patient assessments. For example, nurses can use this information to estimate whether a patient's weight is within a healthy range for their height. This is especially useful in evaluating patients for conditions like obesity or underweight status. However, because the correlation is moderate, it indicates that other factors may also signiﬁcantly inﬂuence weight, such as metabolism, muscle mass, or underlying health conditions. This moderate relationship may prompt a more comprehensive health assessment beyond height and weight alone. WEEK 7 : SEATWORK 2 Week 7 : Seatwork 2 Instructions: Write the letter of the correct answer. 1. Which of the following methods can be used to determine if there is a signiﬁcant linear correlation between two variables? A) Chi-square test B) T-test C) Pearson correlation coefﬁcient D) ANOVA Week 7 : Seatwork 2 Instructions: Write the letter of the correct answer. 2. If two variables have a correlation coefﬁcient of 0.3, what can be inferred about the strength of their linear relationship? A) Strong positive relationship B) Weak positive relationship C) Strong negative relationship D) No relationship Week 7 : Seatwork 2 Instructions: Write the letter of the correct answer. 3. Which of the following values of the correlation coefﬁcient (𝑟) indicates a perfect negative linear relationship between two variables? A) 0.8 B) -1.0 C) 0.0 D) 1.0 Week 7 : Seatwork 2 Instructions: Write the letter of the correct answer. 4. If the correlation coefﬁcient between two variables is 0.65, what does this indicate about their relationship? A) Strong negative correlation B) No correlation C) Moderate positive correlation D) Strong positive correlation Week 7 : Seatwork 2 Instructions: Write the letter of the correct answer. 5. What is the range of values for the Pearson correlation coefﬁcient? A) -1 to 1 B) 0 to 1 C) -∞ to ∞ D) 0 to ∞ Week 7 : Seatwork 2 Instructions: Write the letter of the correct answer. 6. Which statement is true about a correlation coefﬁcient of 0? A) There is a perfect positive linear relationship between the variables. B) There is a perfect negative linear relationship between the variables. C) There is no linear relationship between the variables. D) There is a strong positive linear relationship between the variables. Week 7 : Seatwork 2 Instructions: Write the letter of the correct answer. 7. Which of the following is not a possible outcome when calculating the correlation coefﬁcient? A) 0.5 B) -1.2 C) 0.0 D) 0.8 Week 7 : Seatwork 2 Instructions: Write the letter of the correct answer. 8. What does it mean if the correlation coefﬁcient between two variables is exactly 1? A) There is no linear relationship between the variables. B) There is a perfect negative linear relationship between the variables. C) There is a perfect positive linear relationship between the variables. D) The variables are independent of each other. Week 7 : Seatwork 2 Instructions: Write the letter of the correct answer. 9. Which image shows positive correlation? A) B) C) Week 7 : Seatwork 2 Instructions: Write the letter of the correct answer. 10. Which image shows no correlation? A) B) C) Exchange papers "FAILURE IS A STEP TOWARD SUCCESS, IF YOU LEARN FROM IT." Week 7 : Seatwork 2 Instructions: Write the letter of the correct answer. 1. Which of the following methods can be used to determine if there is a signiﬁcant linear correlation between two variables? A) Chi-square test B) T-test C) Pearson correlation coefﬁcient D) ANOVA Week 7 : Seatwork 2 Instructions: Write the letter of the correct answer. 2. If two variables have a correlation coefﬁcient of 0.3, what can be inferred about the strength of their linear relationship? A) Strong positive relationship B) Weak positive relationship C) Strong negative relationship D) No relationship Week 7 : Seatwork 2 Instructions: Write the letter of the correct answer. 3. Which of the following values of the correlation coefﬁcient (𝑟) indicates a perfect negative linear relationship between two variables? A) 0.8 B) -1.0 C) 0.0 D) 1.0 Week 7 : Seatwork 2 Instructions: Write the letter of the correct answer. 4. If the correlation coefﬁcient between two variables is 0.65, what does this indicate about their relationship? A) Strong negative correlation B) No correlation C) Moderate positive correlation D) Strong positive correlation Week 7 : Seatwork 2 Instructions: Write the letter of the correct answer. 5. What is the range of values for the Pearson correlation coefﬁcient? A) -1 to 1 B) 0 to 1 C) -∞ to ∞ D) 0 to ∞ Week 7 : Seatwork 2 Instructions: Write the letter of the correct answer. 6. Which statement is true about a correlation coefﬁcient of 0? A) There is a perfect positive linear relationship between the variables. B) There is a perfect negative linear relationship between the variables. C) There is no linear relationship between the variables. D) There is a strong positive linear relationship between the variables. Week 7 : Seatwork 2 Instructions: Write the letter of the correct answer. 7. Which of the following is not a possible outcome when calculating the correlation coefﬁcient? A) 0.5 B) -1.2 C) 0.0 D) 0.8 Week 7 : Seatwork 2 Instructions: Write the letter of the correct answer. 8. What does it mean if the correlation coefﬁcient between two variables is exactly 1? A) There is no linear relationship between the variables. B) There is a perfect negative linear relationship between the variables. C) There is a perfect positive linear relationship between the variables. D) The variables are independent of each other. Week 7 : Seatwork 2 Instructions: Write the letter of the correct answer. 9. Which image shows positive correlation? A) B) C) Week 7 : Seatwork 2 Instructions: Write the letter of the correct answer. 10. Which image shows no correlation? A) B) C) Week 7: Weekly Assessment (DURING CLASS) Calculate the Pearson correlation coefﬁcient (𝑟) to determine if there is a linear relationship between the number of hours of sleep and systolic blood pressure in this sample of patients. Round off your answer to at least 2 decimal numbers. Show all your solutions. Use 1 whole Yellow Paper. A nurse wants to study the relationship between the number of hours of sleep and the systolic blood pressure in a group of patients. The data collected is as follows: Patient A: 6 hours of sleep, 140 mmHg blood pressure Patient B: 7 hours of sleep, 130 mmHg blood pressure Patient C: 8 hours of sleep, 120 mmHg blood pressure Patient D: 5 hours of sleep, 150 mmHg blood pressure Patient E: 9 hours of sleep, 110 mmHg blood pressure Week 7: Weekly Assessment (TAKE HOME) Compute the measures of dispersion for the data below. All data are in one set only. Round off your answer to at least 2 decimal numbers. Show all you solutions. Copy and Answer. Use Short Bond Paper. 20 21 30 24 25 24 37 26 22 32 24 30 27 28 29 39 1. Range 2. Interquartile 3. Sample Variance 4. Standard Deviation

Week 7 GEC Math BSN PDF

Document Details

Tags

Related

Summary

Full Transcript

Upgrade to continue