Descriptive Stats - Chapter 2 (Session 5) - Calculations Flashcards
From Page 32, identify the central measure and calculate it for: “The average age of employees in the company is 42 years.”
Statement: Average age is 42 years.
Answer: Mean = 42 (given).
From Page 32, determine the mode for: “The most frequently sold shoe size in the store is size 8.”
Statement: Most frequent shoe size is 8.
Answer: Mode = 8 (given).
From Page 32, find the median for the statement: “Half of the students scored more than 75% in the mathematics test” (assume scores: 60, 70, 75, 80, 90).
Assumed data: 60, 70, 75, 80, 90
Ordered: 60, 70, 75, 80, 90
Median = 75 (3rd value)
Calculate the mean of the dataset: 3, 7, 2, 9, 5 (Page 18).
Data: 3, 7, 2, 9, 5
Sum = 3 + 7 + 2 + 9 + 5 = 26
Mean = 26 / 5 = 5.2
Find the median of the dataset: 3, 7, 2, 9, 5 (Page 18).
Ordered: 2, 3, 5, 7, 9
Median = 5 (3rd value)
Answer: 5
Determine the mode of the dataset: 3, 7, 2, 9, 5 (Page 18).
No repeats
Answer: No mode
From Page 18, calculate the range for: 58, 50, 33, 51, 38, 43, 60, 55, 46, 43.
Data: 58, 50, 33, 51, 38, 43, 60, 55, 46, 43
Range = 60 - 33 = 27
From Page 31, find the range for: 18, 19, 21, 21, 22, 35, 13, 23.
Data: 18, 19, 21, 21, 22, 35, 13, 23
Range = 35 - 13 = 22
Answer: 22
Calculate the range for the exam scores: 77, 85, 92, 64, 78, 95, 82 (Page 31).
Data: 77, 85, 92, 64, 78, 95, 82
Range = 95 - 64 = 31
Answer: 31
Find the range for the temperatures: 18, 22, 19, 25, 12 (Page 31).
Data: 18, 22, 19, 25, 12
Range = 25 - 12 = 13
Answer: 13
From Page 20, calculate the IQR for: 1, 3, 5, 7, 9, 11, 13, 15.
Data: 1, 3, 5, 7, 9, 11, 13, 15
Q1 = 3 + 5 / 2 = 4, Q3 = 11 + 13 / 2 = 12
IQR = 12 - 4 = 8
Answer: 8
From Page 20, find the quartile deviation for: 1, 3, 5, 7, 9, 11, 13, 15.
Q1 = 4, Q3 = 12
Quartile Deviation = (12 - 4) / 2 = 4
Answer: 4
From Page 28, verify the IQR for salaries: 2200, 2500, 2900, 3200, 3500, 3800, 4100, 4500, 5000, 5500.
Q1 = 4, Q3 = 12
Quartile Deviation = (12 - 4) / 2 = 4
Answer: 4
From Page 28, calculate the quartile deviation for the salaries above.
Q1 = 2900, Q3 = 4500
Quartile Deviation = (4500 - 2900) / 2 = 800
Answer: 800
Find the IQR for exam scores: 77, 85, 92, 64, 78, 95, 82 (Page 31).
Data: 77, 85, 92, 64, 78, 95, 82
Ordered: 64, 77, 78, 82, 85, 92, 95
Q1 = 77, Q3 = 92
IQR = 92 - 77 = 15
Answer: 15
From Page 25, calculate the population variance for exam scores: 92, 95, 85, 80, 75, 50.
Data: 92, 95, 85, 80, 75, 50
Mean = (92 + 95 + 85 + 80 + 75 + 50) / 6 = 477 / 6 = 79.5
Variance = [(92-79.5)² + (95-79.5)² + (85-79.5)² + (80-79.5)² + (75-79.5)² + (50-79.5)²] / 6
= (156.25 + 240.25 + 30.25 + 0.25 + 20.25 + 870.25) / 6 = 1317.5 / 6 ≈ 219.58
Answer: 219.58
From Page 25, find the population standard deviation for the same scores.
SD = √219.58 ≈ 14.82
Answer: 14.82
From Page 26, calculate the sample variance for: 58, 50, 33, 51, 38, 43, 60, 55, 46, 43.
Data: 58, 50, 33, 51, 38, 43, 60, 55, 46, 43
Mean = (58 + 50 + 33 + 51 + 38 + 43 + 60 + 55 + 46 + 43) / 10 = 477 / 10 = 47.7
Variance = [(58-47.7)² + (50-47.7)² + … + (43-47.7)²] / (10-1)
= (106.09 + 5.29 + 214.09 + 11.29 + 92.29 + 22.09 + 155.29 + 53.29 + 2.89 + 22.09) / 9 = 684.61 / 9 ≈ 76.07
Answer: 76.07
From Page 26, find the sample standard deviation for the electricity consumption data above.
SD = √76.07 ≈ 8.72
Answer: 8.72 kWh
From Page 31, calculate the standard deviation for temperatures: 18, 22, 19, 25, 12.
Data: 18, 22, 19, 25, 12
Mean = (18 + 22 + 19 + 25 + 12) / 5 = 96 / 5 = 19.2
Variance = [(18-19.2)² + (22-19.2)² + (19-19.2)² + (25-19.2)² + (12-19.2)²] / 4
= (1.44 + 7.84 + 0.04 + 33.64 + 51.84) / 4 = 94.8 / 4 = 23.7
SD = √23.7 ≈ 4.87 (Note: Document says 4.35, assuming sample SD)
Answer: 4.87 (corrected)
