A series of houses are surveyed and found to have 1, 2, 2, 2, 3, 4, 4, 6. 7 children respectively. Find the mean median and mode of the following:
## Core Concept
The problem involves calculating three important statistical measures: mean, median, and mode, from a given dataset of the number of children in a series of houses. The mean is the average value, the median is the middle value when the data is arranged in ascending order, and the mode is the value that appears most frequently.
## Why the Correct Answer is Right
To find the mean, we sum all the values and divide by the number of values: (1 + 2 + 2 + 2 + 3 + 4 + 4 + 6 + 7) / 9 = 31 / 9 = 3.44. To find the median, we arrange the data in ascending order: 1, 2, 2, 2, 3, 4, 4, 6, 7. Since there are 9 values (an odd number), the median is the 5th value, which is 3. To find the mode, we identify the value that appears most frequently, which is 2 (appears three times). Therefore, the mean is 3.44, the median is 3, and the mode is 2.
## Why Each Wrong Option is Incorrect
- **Option A:** This option is incorrect because it does not match the calculated values of mean, median, and mode.
- **Option B:** This option is incorrect because, similar to option A, it does not correspond with the calculated statistical measures.
- **Option D:** This option is incorrect as it also does not match the calculated values.
## Clinical Pearl / High-Yield Fact
In statistics, understanding the mean, median, and mode is crucial as they provide different insights into the distribution of data. The mean is sensitive to outliers, the median is useful for skewed distributions, and the mode can be helpful for categorical data or when the most common value is needed.
## Correct Answer Line
**Correct Answer: C.**