worksheet 2

Worksheet 2 Study Notes

Question 1: Body Temperature Data of 15 Participants

• Data Points: 36.2, 37.1, 38.0, 36.8, 37.5, 35.9, 39.1, 36.4, 37.8, 38.3, 36.6, 37.0, 39.4, 36.1, 38.6

a. Calculate and Interpret the Mean

• Formula for Mean:
  $ext{Mean} = \frac{ ext{Sum of all values}}{ ext{Number of values}}$
• Calculations:
  • Sum of values = 36.2 + 37.1 + 38.0 + 36.8 + 37.5 + 35.9 + 39.1 + 36.4 + 37.8 + 38.3 + 36.6 + 37.0 + 39.4 + 36.1 + 38.6 = 562.2
  • Number of values = 15
  • Mean = $\frac{562.2}{15} = 37.48$
• Interpretation:
  The mean body temperature of the participants is approximately 37.5°C, indicating a typical average healthy body temperature.

b. Calculate and Interpret the Median

• Definition of Median: The median is the middle value when data is ordered from lowest to highest. If there is an even number of observations, it is the average of the two middle numbers.
• Ordered Data: 35.9, 36.1, 36.2, 36.4, 36.6, 36.8, 37.0, 37.1, 37.5, 37.8, 38.0, 38.3, 38.6, 39.1, 39.4
• Calculations:
  The middle value (8th term) for 15 data points is 37.1.
• Interpretation:
  The median body temperature is 37.1°C, which indicates that half of the participants have a body temperature below this value and half are above.

Question 2: Weekly Screen Time of 30 High School Students

• Data Points: 6, 4, 9, 5, 7, 3, 20, 6, 8, 4, 5, 6, 2, 7, 5, 9, 6, 3, 8, 10, 4, 7, 6, 8, 5, 6, 7, 4, 6, 5

a. Create a Simple Frequency Distribution

• Frequency Distribution Table:
  

• Mean Calculation:
  • Sum of values = 6 + 4 + 9 + 5 + 7 + 3 + 20 + 6 + 8 + 4 + 5 + 6 + 2 + 7 + 5 + 9 + 6 + 3 + 8 + 10 + 4 + 7 + 6 + 8 + 5 + 6 + 7 + 4 + 6 + 5 = 6 + 20 + 31 + 22 + 23 + 10 = 195
  • Mean = $\frac{195}{30} = 6.5$
• Interpretation:
  The average screen time is 6.5 hours per week.
• Median Calculation:
  • Ordered Data: 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10, 20
  • Median value (15th term for 30 data points) is 6, since there are 15 data points each above and below.
• Mode Calculation: Mode is the most frequent value, which is 6 (occurs 6 times).
• Interpretation:
  • Mean: Average screen time is 6.5 hours.
  • Median: The middle point of data shows 6 hours.
  • Mode: The most common screen time among students is 6 hours.

c. Identifying Outliers and Best Measure of Central Tendency

• Outlier Analysis:
  • Outlier detected: 20 hours, significantly higher than others.
• Best Measure of Central Tendency:
  • The best measure for this dataset is the median due to the presence of an outlier that skews the mean.

Question 3: Resting Heart Rate of 45 Participants

• Data Points: 72, 68, 75, 80, 64, 70, 78, 85, 66, 74, 69, 71, 77, 82, 60, 65, 73, 79, 88, 67, 76, 83, 62, 58, 90, 84, 61, 63, 81, 86, 59, 87, 55, 92, 57, 89, 56, 91, 54, 93, 52, 95, 53, 94, 51

a. Create a Grouped Frequency Distribution Using Five Classes

• Class Boundaries: 50-59, 60-69, 70-79, 80-89, 90-99


• Frequency Distribution Table:
  

• Mean Calculation:
  • Sum of values = 72 + 68 + 75 + … + 54 + 93 + 52 + 95 + 53 + 94 + 51 = 3491
  • Mean = $\frac{3491}{45} ext{ (total number of values)} ext{which results in approximately } 77.8$
• Interpretation:
  The mean resting heart rate is approximately 77.8 bpm.
• Median Calculation:
  • Ordered Data: 51, 52, 53, …, 95
  • Median value: 77 (23rd term for 45 data points)
• Mode Calculation:
  • Mode: No mode, as most values are unique.

Question 4: Appropriate Measures of Central Tendency

1. Household Incomes Study

• Measure of Central Tendency: Median
• Justification:
  The median reduces the effect of outliers that may skew the average, providing a more representative measure of typical income.

2. High School Students’ Grades

• Measure of Central Tendency: Mode
• Justification:
  Mode gives the most frequent grade, which helps in understanding the common performance level without complex analysis.

3. Patients’ Blood Pressure Readings

• Measure of Central Tendency: Mean
• Justification:
  Without extreme values, the mean offers a clear average reading regarding general patient blood pressure levels.

4. Marketing Company Phone Brands Study

• Measure of Central Tendency: Mode
• Justification:
  Mode succinctly conveys the most popular brand among teenagers, which is straightforward and easily interpretable.