Statistics – Mean, Median, Mode, Dispersion Quiz - ICSE Class 11 Mathematics
Free practice quiz: Statistics – Mean, Median, Mode, Dispersion (ICSE Class 11 Mathematics). 60 multiple-choice questions with answers and explanations. Play online, no sign-up needed.
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For a dataset with 100 observations, the sum of deviations from the mean is always:
- Zero
- Equal to the mean
- Equal to the median
- Cannot be determined
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Answer: A. Zero
The sum of deviations of individual observations from their arithmetic mean is always zero. This is a fundamental property of the mean.
Consider the dataset: {5, 15, 25, 35, 45}. If we add the value 55 to this dataset, how does the median change?
- It remains unchanged
- It increases by 5
- It increases by 10
- It decreases
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Answer: B. It increases by 5
The original dataset is {5, 15, 25, 35, 45}. There are 5 observations. The median is the 3rd element, which is 25. When 55 is added, the dataset becomes {5, 15, 25, 35, 45, 55}. There are now 6 observations. The median is the average of the 3rd and 4th elements, which are 25 and 35. The new median is (25 + 35) / 2 = 60 / 2 = 30. The median has increased from 25 to 30, an increase of 5.
For a dataset, if Q1 = 10, Median (Q2) = 25, and Q3 = 40, what is the interquartile range (IQR)?
- 15
- 25
- 30
- 35
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Answer: C. 30
The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). IQR = Q3 - Q1. Given Q1 = 10 and Q3 = 40, the IQR = 40 - 10 = 30.
What does the interquartile range measure?
- The total spread of the data
- The spread of the middle 50% of the data
- The average deviation from the mean
- The frequency of the most common value
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Answer: B. The spread of the middle 50% of the data
The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). It represents the range of the middle half of the data, providing a measure of spread that is less affected by outliers than the total range.
If the mean of a dataset is 50 and the sum of deviations from the mean is 150, what is the number of observations?
- 15
- 5
- 10
- Cannot be determined
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Answer: D. Cannot be determined
A fundamental property of the mean is that the sum of the deviations of each observation from the mean is always zero. If the sum of deviations is stated as 150, this implies an error in the premise of the question, as it contradicts a core statistical property. Therefore, the number of observations cannot be determined from this erroneous information.