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Questions and Answers
What is the total surface area of a solid hemisphere with radius $r$?
What is the total surface area of a solid hemisphere with radius $r$?
- $6\pi r^2$
- $3\pi r^2$ (correct)
- $2\pi r^2$
- $4\pi r^2$
What is the median class of the following frequency table?
Class-interval
Frequency
0-10
2
10-20
8
20-30
12
30-40
18
40-50
10
What is the median class of the following frequency table?
| Class-interval | Frequency |
|---|---|
| 0-10 | 2 |
| 10-20 | 8 |
| 20-30 | 12 |
| 30-40 | 18 |
| 40-50 | 10 |
- 20-30
- 30-40 (correct)
- 40-50
- 10-20
The mean and median of a frequency table are 30 and 35 respectively. What is the approximate mode?
The mean and median of a frequency table are 30 and 35 respectively. What is the approximate mode?
- 35
- 40
- 55
- 45 (correct)
If an event occurs with certainty, what is its probability?
If an event occurs with certainty, what is its probability?
What is the probability of an impossible event?
What is the probability of an impossible event?
Flashcards
Surface Area of Hemisphere
Surface Area of Hemisphere
The total surface area of a hemisphere is the sum of the areas of its curved surface and its flat circular base. The curved surface area is half the surface area of a sphere with the same radius. The flat circular base has an area equal to πr^2, where r is the radius. Therefore, the total surface area of a hemisphere is (1/2)(4πr^2) + πr^2 = 3πr^2.
Median Class
Median Class
The median class is the class interval containing the median of a frequency distribution. To find the median class, first calculate the cumulative frequencies. The median class is the class interval whose cumulative frequency is greater than or equal to half the total frequency.
Mean, Median, and Mode Relationship
Mean, Median, and Mode Relationship
In a skewed distribution, the mean, median, and mode are not necessarily equal. In general, the mean is pulled towards the tail of the distribution, the median is less affected, and the mode is at the peak. If the mean is greater than the median, the distribution is positively skewed. If the mean is less than the median, the distribution is negatively skewed.
Probability of a Certain Event
Probability of a Certain Event
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Probability of an Event
Probability of an Event
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Study Notes
Total Surface Area of a Solid Hemisphere
- The total surface area of a solid hemisphere with radius 'r' is 3πr².
Median Class
- To find the median class, first arrange the class intervals in ascending order.
- The class interval with the cumulative frequency greater than or equal to half of the total frequency is the median class.
Mean and Median
- If the mean and median of a frequency table are 30 and 35, respectively, then the mode will be 48.
Probability of a Certain Event
- If an event is certain to occur, its probability is 1.
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