9 families surveyed have 1, 2,2, 2,3,4, 4, 6, 7 children respectively. The mean, median, mode respectively are –
## **Core Concept**
The question involves calculating and understanding three important statistical measures: mean, median, and mode, in the context of a survey about the number of children in families.
## **Why the Correct Answer is Right**
To find the mean, we sum up all the children: 1 + 2 + 2 + 2 + 3 + 4 + 4 + 6 + 7 = 31, and then divide by the number of families, which is 9. So, the mean is 31 / 9 = 3.44. To find the median, we first arrange the numbers in ascending order: 1, 2, 2, 2, 3, 4, 4, 6, 7. Since there are 9 numbers (an odd number), the median is the middle number, which is the 5th number: 3. The mode is the number that appears most frequently, which in this case is 2 since it appears three times. Therefore, the mean, median, and mode are approximately 3.44, 3, and 2 respectively.
## **Why Each Wrong Option is Incorrect**
- **Option A:** This option does not match our calculated values for mean, median, and mode.
- **Option B:** Similarly, this does not match our calculations.
- **Option D:** This also does not correspond with the values we found.
## **Clinical Pearl / High-Yield Fact**
In statistics, understanding the mean, median, and mode is crucial as they describe different aspects of a dataset's central tendency. 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:** .