# Summarizing Quantitative Data - Grade 9 Statistics & Probability Worksheet
Section A: Multiple Choice Questions
Q1: A dataset consists of the following values: 12, 15, 18, 15, 20, 15, 22. What is the mode of this dataset? (a) 15 (b) 17 (c) 18 (d) 20
Solution:
Ans: (a) Explanation: The mode is the value that appears most frequently in a dataset. In this case, 15 appears three times, which is more than any other value. Therefore, the mode is 15.
Q2: The mean of five numbers is 24. If four of the numbers are 20, 22, 26, and 28, what is the fifth number? (a) 18 (b) 24 (c) 22 (d) 26
Solution:
Ans: (b) Explanation: The mean formula is \(\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}\). Given: Mean = 24 and number of values = 5 Therefore: Sum = 24 × 5 = 120 Sum of four known numbers = 20 + 22 + 26 + 28 = 96 Fifth number = 120 - 96 = 24
Q3: Which measure of central tendency is most affected by extreme values (outliers)? (a) Mode (b) Median (c) Mean (d) Range
Solution:
Ans: (c) Explanation: The mean is calculated using all values in the dataset, so extreme values greatly influence it. The median and mode are resistant to outliers. The range is a measure of spread, not central tendency, though it is also affected by outliers.
Q4: The following data represents test scores: 65, 70, 75, 80, 85. What is the median score? (a) 70 (b) 75 (c) 80 (d) 77.5
Solution:
Ans: (b) Explanation: The median is the middle value when data is arranged in order. Since there are 5 values (odd number), the median is the 3rd value, which is 75.
Q5: A dataset has the following values: 5, 8, 12, 15, 20. What is the range of this dataset? (a) 5 (b) 12 (c) 15 (d) 25
Solution:
Ans: (c) Explanation: The range is calculated as: Range = Maximum value - Minimum value = 20 - 5 = 15. This measure shows the spread of the data.
Q6: Which of the following datasets has the greatest variability? (a) 10, 12, 13, 14, 15 (b) 5, 10, 15, 20, 25 (c) 20, 21, 22, 23, 24 (d) 15, 15, 15, 15, 15
Solution:
Ans: (b) Explanation:Variability measures how spread out the data is. Dataset (b) has a range of 20 (25 - 5), which is the largest. Dataset (a) has range 5, dataset (c) has range 4, and dataset (d) has range 0.
Q7: The interquartile range (IQR) is calculated as: (a) Q3 - Q1 (b) Q2 - Q1 (c) Maximum - Minimum (d) Q3 + Q1
Solution:
Ans: (a) Explanation: The interquartile range (IQR) measures the spread of the middle 50% of the data and is calculated as \(\text{IQR} = Q_3 - Q_1\), where \(Q_3\) is the third quartile and \(Q_1\) is the first quartile.
Q8: A box plot displays which of the following statistical measures? (a) Mean, mode, and range (b) Minimum, Q1, median, Q3, and maximum (c) Mean, median, and standard deviation (d) Frequency and relative frequency
Solution:
Ans: (b) Explanation: A box plot (or box-and-whisker plot) displays the five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. This provides a visual representation of the distribution and spread of data.
Section B: Fill in the Blanks
Q9: The __________ is the value that separates the higher half from the lower half of a dataset when arranged in order.
Solution:
Ans: median Explanation: The median is the middle value of an ordered dataset and divides the data into two equal halves.
Q10: The first quartile (Q1) represents the __________ percentile of the data.
Solution:
Ans: 25th Explanation: The first quartile (Q1) marks the point below which 25% of the data falls, making it the 25th percentile.
Q11: In a symmetric distribution, the mean and median are __________.
Solution:
Ans: equal (or approximately equal) Explanation: In a symmetric distribution, the data is evenly distributed around the center, so the mean and median have the same or very similar values.
Q12: The measure of spread that is calculated by finding the difference between the third and first quartiles is called the __________.
Solution:
Ans: interquartile range (or IQR) Explanation: The interquartile range (IQR) is \(Q_3 - Q_1\) and represents the spread of the middle 50% of the data, making it resistant to outliers.
Q13: A dataset with values that are all the same has a standard deviation of __________.
Solution:
Ans: 0 (or zero) Explanation:Standard deviation measures variability. When all values are identical, there is no variability, so the standard deviation equals zero.
Q14: An outlier is a data value that is significantly __________ or __________ than most other values in the dataset.
Solution:
Ans: higher, lower (or lower, higher) Explanation: An outlier is an extreme value that differs substantially from the rest of the data, either being much higher or much lower than typical values.
Section C: Word Problems
Q15: The ages of seven students in a study group are: 14, 15, 14, 16, 15, 14, and 17 years. Calculate the mean age of the students.
Solution:
Ans: Sum of ages = 14 + 15 + 14 + 16 + 15 + 14 + 17 = 105 Number of students = 7 Mean = \(\frac{105}{7}\) = 15 Final Answer: 15 years
Q16: A basketball player scored the following points in six games: 18, 22, 19, 25, 22, and 20. Find the median number of points scored.
Solution:
Ans: First, arrange the data in order: 18, 19, 20, 22, 22, 25 Since there are 6 values (even number), the median is the average of the 3rd and 4th values: Median = \(\frac{20 + 22}{2}\) = \(\frac{42}{2}\) = 21 Final Answer: 21 points
Q17: The following are the daily temperatures (in °F) recorded over one week: 68, 72, 70, 75, 73, 71, 69. Calculate the range of the temperatures.
Solution:
Ans: Maximum temperature = 75°F Minimum temperature = 68°F Range = 75 - 68 = 7 Final Answer: 7°F
Q18: The quiz scores of 9 students are: 72, 85, 90, 78, 85, 88, 92, 85, 80. Determine the mode of the quiz scores.
Solution:
Ans: Count the frequency of each score: 72 appears 1 time 78 appears 1 time 80 appears 1 time 85 appears 3 times 88 appears 1 time 90 appears 1 time 92 appears 1 time The value 85 appears most frequently (3 times). Final Answer: 85
Q19: A dataset of exam scores has a minimum of 55, Q1 = 68, median = 75, Q3 = 82, and maximum of 95. Calculate the interquartile range (IQR) of the exam scores.
Q20: The heights (in inches) of five plants are: 12, 15, 18, 14, and 16. If a sixth plant with a height of 45 inches is added to the group, how does this affect the mean? Calculate both the original mean and the new mean.
Solution:
Ans: Original mean: Sum = 12 + 15 + 18 + 14 + 16 = 75 Number of plants = 5 Original mean = \(\frac{75}{5}\) = 15 inches
New mean (with the sixth plant): New sum = 75 + 45 = 120 Number of plants = 6 New mean = \(\frac{120}{6}\) = 20 inches
The outlier (45 inches) significantly increased the mean from 15 to 20 inches. Final Answer: Original mean = 15 inches; New mean = 20 inches
The document Worksheet (with Solutions): Summarizing Quantitative Data is a part of the Grade 9 Course Statistics & Probability.
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