# Worksheet: Displaying and Comparing Quantitative Data
## Section A: Multiple Choice Questions
Q1: A dataset shows the number of hours students spent studying: 2, 3, 3, 4, 5, 5, 5, 6, 7, 8. What is the median of this dataset? (a) 4 (b) 5 (c) 4.5 (d) 6
Solution:
Ans: (b) Explanation: To find the median, arrange the data in order (already done) and find the middle value. Since there are 10 values (even number), the median is the average of the 5th and 6th values: \(\frac{5 + 5}{2} = 5\).
Q2: Which measure of center is most affected by outliers in a dataset? (a) Median (b) Mode (c) Mean (d) Range
Solution:
Ans: (c) Explanation: The mean is calculated by adding all values and dividing by the count, so extreme values (outliers) significantly affect it. The median and mode are resistant to outliers. Range is a measure of spread, not center.
Q3: A box plot shows that Q1 = 15 and Q3 = 35. What is the interquartile range (IQR)? (a) 15 (b) 20 (c) 35 (d) 50
Solution:
Ans: (b) Explanation: The interquartile range (IQR) is calculated as \(Q3 - Q1 = 35 - 15 = 20\). The IQR measures the spread of the middle 50% of the data.
Q4: Which type of graph is most appropriate for displaying the distribution of a single quantitative variable? (a) Bar graph (b) Histogram (c) Pie chart (d) Line graph
Solution:
Ans: (b) Explanation: A histogram displays the distribution of quantitative data by showing frequencies of data intervals. Bar graphs are for categorical data, pie charts show parts of a whole, and line graphs show trends over time.
Q5: A distribution is skewed to the right. Which statement is most likely true? (a) Mean <> (b) Mean = Median (c) Mean > Median (d) Mode > Mean
Solution:
Ans: (c) Explanation: In a right-skewed distribution, the tail extends to the right with high values pulling the mean upward, so Mean > Median. The mean is affected by extreme values while the median remains in the center of the data.
Q6: The standard deviation of a dataset is 0. What does this tell you about the data? (a) The data has one outlier (b) All data values are the same (c) The data is normally distributed (d) The mean equals zero
Solution:
Ans: (b) Explanation: A standard deviation of 0 means there is no variation in the data, so all values must be identical. Standard deviation measures spread from the mean, and zero spread means no differences among values.
Q7: Which of the following values cannot be a percentile? (a) 25 (b) 50 (c) 75 (d) 110
Solution:
Ans: (d) Explanation:Percentiles range from 0 to 100, representing the percentage of data below a certain value. A value of 110 is impossible because it would mean 110% of the data falls below that point, which is mathematically impossible.
Q8: Two datasets have the same mean but different standard deviations. Dataset A has a standard deviation of 2, and Dataset B has a standard deviation of 8. Which statement is true? (a) Dataset A has more variability than Dataset B (b) Dataset B has more variability than Dataset A (c) Both datasets have the same spread (d) The medians must be equal
Solution:
Ans: (b) Explanation:Standard deviation measures variability or spread. A larger standard deviation indicates greater variability. Dataset B with SD = 8 has more spread than Dataset A with SD = 2, meaning its values are more dispersed from the mean.
## Section B: Fill in the Blanks
Q9: The __________ is the difference between the maximum and minimum values in a dataset.
Solution:
Ans: range Explanation: The range is a simple measure of spread calculated as maximum value minus minimum value, showing the total span of the data.
Q10: In a box plot, the box represents the __________ percent of the data.
Solution:
Ans: 50 (or middle 50) Explanation: The box in a box plot extends from Q1 to Q3, containing the middle 50% of the data, also known as the interquartile range.
Q11: A distribution with two peaks is called __________.
Solution:
Ans: bimodal Explanation: A bimodal distribution has two distinct peaks or modes, indicating two different groups or common values within the dataset.
Q12: The __________ is the value that appears most frequently in a dataset.
Solution:
Ans: mode Explanation: The mode is the measure of center that identifies the most common value(s) in a dataset and can be used for both quantitative and categorical data.
Q13: If a dataset is symmetric, the mean and median are approximately __________.
Solution:
Ans: equal (or the same) Explanation: In a symmetric distribution, the data is balanced around the center, causing the mean and median to have approximately the same value.
Q14: The __________ measures the average distance of each data point from the mean.
Solution:
Ans: standard deviation Explanation: The standard deviation quantifies how much individual data values typically deviate from the mean, providing a measure of spread or variability.
## Section C: Word Problems
Q15: The test scores of 12 students in a statistics class are: 78, 82, 85, 85, 88, 90, 90, 90, 92, 95, 95, 100. Calculate the mean score for the class.
Solution:
Ans:
Sum of scores = \(78 + 82 + 85 + 85 + 88 + 90 + 90 + 90 + 92 + 95 + 95 + 100 = 1070\)
Mean = \(\frac{1070}{12} = 89.17\) Final Answer: 89.17
Q16: A dataset of daily temperatures (in °F) for a week is: 68, 70, 72, 74, 76, 78, 95. Identify whether 95 is an outlier using the 1.5 × IQR rule.
Solution:
Ans:
Ordered data: 68, 70, 72, 74, 76, 78, 95
Q1 = 70, Q3 = 78
IQR = \(78 - 70 = 8\)
Upper fence = \(Q3 + 1.5 \times IQR = 78 + 1.5 \times 8 = 78 + 12 = 90\)
Since 95 > 90, it is an outlier. Final Answer: Yes, 95 is an outlier
Q17: The heights (in inches) of 8 basketball players are: 70, 72, 73, 74, 75, 76, 77, 80. Find the first quartile (Q1) and third quartile (Q3) of this dataset.
Solution:
Ans:
Data is already ordered: 70, 72, 73, 74, 75, 76, 77, 80
Median position: between 4th and 5th values
Lower half: 70, 72, 73, 74
Q1 = \(\frac{72 + 73}{2} = 72.5\)
Upper half: 75, 76, 77, 80
Q3 = \(\frac{76 + 77}{2} = 76.5\) Final Answer: Q1 = 72.5 inches, Q3 = 76.5 inches
Q18: The number of books read by 10 students during summer break are: 3, 5, 5, 6, 7, 8, 8, 8, 9, 11. Create a frequency table showing how many students read each number of books, then identify the mode.
Solution:
Ans:
Frequency table:
3 books: 1 student
5 books: 2 students
6 books: 1 student
7 books: 1 student
8 books: 3 students
9 books: 1 student
11 books: 1 student
The mode is the value with highest frequency. Final Answer: Mode = 8 books
Q19: A company recorded the number of customer complaints per day for 15 days: 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 8, 9, 10, 25. Compare the mean and median. Which measure better represents the typical number of complaints? Explain your reasoning.
Solution:
Ans:
Median (8th value in ordered list) = 5
Mean = \(\frac{2+3+3+4+4+5+5+5+6+6+7+8+9+10+25}{15} = \frac{102}{15} = 6.8\)
The value 25 is an outlier that pulls the mean upward.
The median (5) better represents typical complaints because it is resistant to the outlier. Final Answer: Median = 5, Mean = 6.8; the median better represents the typical number of complaints because it is not affected by the outlier value of 25
Q20: Two classes took the same math test. Class A has a mean score of 85 with a standard deviation of 3. Class B has a mean score of 85 with a standard deviation of 10. Which class has more consistent test scores? Justify your answer.
Solution:
Ans:
Both classes have the same mean (85), but different standard deviations.
Standard deviation measures consistency (variability).
Class A: SD = 3 (lower variability, scores closer to mean)
Class B: SD = 10 (higher variability, scores more spread out)
Lower standard deviation indicates more consistency. Final Answer: Class A has more consistent test scores because it has a smaller standard deviation (3 vs. 10), meaning scores are closer to the mean
The document Worksheet (with Solutions): Displaying and Comparing Quantitative Data is a part of the Grade 9 Course Statistics & Probability.
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