Question 1: Calculate the five-number summary for the data set: 4, 7, 2, 9, 5, 3, 8.

Answer: [Answer: Min=2, Q1=3, Median=5, Q3=8, Max=9]

Question 2: Construct a box plot for the data: 12, 15, 11, 14, 13, 16, 12.

Answer: Constructed on the grid with min=11, Q1=12, Median=14, Q3=15, Max=16

Question 3: Find the median and interquartile range (IQR) of the data set: 22, 30, 25, 28, 26, 24, 29.

Answer: [Median: 26, IQR: 29 - 24 = 5]

Question 4: What is the five-number summary for the scores: 55, 60, 58, 62, 59, 57, 61?

Answer: [Min=55, Q1=57, Median=59, Q3=61, Max=62]

Question 5: Calculate the lower quartile (Q1) for the data set: 3, 7, 5, 9, 2, 6, 4.

Answer: [Q1=3]

Question 1: A teacher records the test scores of 20 students. The five-number summary is: Min=42, Q1=50, Median=55, Q3=60, Max=75. Explain what this tells you about the distribution of scores and identify any potential outliers.

Answer: The scores are spread with a lower bound at 42 and an upper at 75. The median at 55 indicates half scored below and half above. Q1 and Q3 show the middle 50% are between 50 and 60. The range is large, and the difference between max and Q3 may suggest outliers above 75 or a skewed distribution.

Question 2: Given the data set: 8, 12, 15, 10, 14, 13, 11, find the five-number summary and draw the corresponding box plot. Show your working.

Answer: [Min=8, Q1=10, Median=13, Q3=15, Max=15]

Question 1: A bakery records the number of bread loaves sold each day for a week: 30, 45, 35, 50, 40, 55, 60. Find the five-number summary and interpret what it reveals about daily sales.

Answer: Summary: Min=30, Q1=35, Median=40, Q3=55, Max=60. It shows most sales are between 35 and 55, with some days selling as few as 30 or as many as 60.

Question 2: The heights (cm) of a group of students are recorded as: 150, 160, 155, 165, 158, 162, 159. Calculate the five-number summary and explain what it indicates about the group's heights.

Answer: [Min=150, Q1=155, Median=158, Q3=162, Max=165]

Question 1: Given the data set: 5, 7, 9, 3, 4, 8, 10, 12, 6. Calculate the five-number summary and identify any outliers using the 1.5*IQR rule.

Answer: Summary: Min=3, Q1=4, Median=7, Q3=9, Max=12. IQR=5, outliers are any data beyond Q1-1.5*IQR= -3.5 or Q3+1.5*IQR= 16.5, so none outliers.

Question 2: Construct a box plot for the following data: 20, 25, 22, 28, 24, 30, 26, 35, 40. Include all five points and justify your construction.

Answer: Constructed with Min=20, Q1=22, Median=26, Q3=30, Max=40 on the grid. The box spans from 22 to 30, with median at 26, and whiskers extend to 20 and 40.

Question 1: Explain why the median and the interquartile range are important in understanding data distribution.

Answer: They help identify the center of the data and the spread of the middle 50%, providing insight into data skewness and variability.

Question 2: A data set has a very high maximum value compared to the median. What might this indicate about the data's distribution?

Answer: It suggests the data may be positively skewed with outliers or unusually high values.

Question 1: Student's answer: The range is calculated as Max minus Min, so 100 - 60 = 40. However, they said the range is 50. Identify the mistake and provide the correct range.

Answer: The mistake is in subtraction; 100 minus 60 equals 40, not 50. The correct range is 40.