Understanding Positional Averages in Statistics
The question asks us to identify which measure among the given options is a positional average. A positional average is a measure of central tendency whose value depends upon its position in the statistical arrangement of the data. Let's analyze each option:
Analyzing Different Types of Averages
- Arithmetic Mean: This is calculated by summing all the values in a dataset and dividing by the number of values. For example, the mean of {2, 4, 6} is \(\frac{2 + 4 + 6}{3} = 4\). It depends on the actual numerical values of all data points, not just their position.
- Median: The median is the middle value of a dataset when it is sorted in ascending or descending order. If there is an even number of observations, the median is the average of the two middle values. For example, in the sorted dataset {2, 4, 6, 8, 10}, the median is 6, which is the middle value (3rd position). In the sorted dataset {2, 4, 6, 8}, the median is \(\frac{4 + 6}{2} = 5\), the average of the two middle values (2nd and 3rd positions). The calculation of the median relies solely on the position of the data points after sorting.
- Mode: The mode is the value that appears most frequently in a dataset. For example, in the dataset {2, 4, 4, 6, 8}, the mode is 4 because it appears twice, more than any other value. The mode is determined by frequency, not position in a sorted list.
- Geometric Mean: This is calculated by taking the nth root of the product of n values. For example, the geometric mean of {2, 4, 8} is \(\sqrt[3]{2 \times 4 \times 8} = \sqrt[3]{64} = 4\). Like the arithmetic mean, it depends on the actual values of the data points.
Identifying the Positional Average
Based on the definitions:
- Arithmetic Mean: Not a positional average.
- Median: Is a positional average because its value is determined by its position in the sorted data.
- Mode: Not a positional average.
- Geometric Mean: Not a positional average.
Therefore, the Median is the positional average among the given options.
Similar Questions
What is the median of the distribution ?
- What is the mode of the distribution?
- Consider the following data :
110, 41, 43, 95, 127, 99, 61, 92, 71, 93, 110, 36.
If 93 is replaced by 94, then consider the following statements:
1. The difference between new median and old median is 1.
2. The difference between new mean and old mean is less than 0·1.
3. The difference between new mode and old mode is zero.
Which of the statements given above are correct? - Which measure of central tendency is least affected by the presence of extreme observations in the data?
- To find the average ratio like price/unit, work done/hour, kilometre/hour under certain conditions, the suitable measure of central tendency applicable is
- The frequency distribution of marks of 100 candidates in a particular examination is as follows:What are the average marks of the candidates?
Marks Number of Candidates More than 10 100 More than 20 75 More than 30 60 More than 40 40 - The arithmetic mean of 200 observations is 60. If 5 is multiplied to each observation, then what will be the new arithmetic mean?
- A distribution consists of 3 components with frequencies 45, 40 and 55 having their means 2, 2.5 and 2 respectively. What is the mean of the combined distribution?
- What is the value of \(u\)?
- What is the value of \(v\)?
Important Questions from Elementary Statistics
In a colony 5 families have 1 child, 7 families have 2 children, 8 families have 3 children and 3 families have 4 children.What is the mode of the number of children.
For which set of numbers do the mean, median and mode all have the same value?
The median of 5, 8, 25, 22, 34, 18 is
Find the mean of first 5 two-digit multiples of 4.
The difference between the upper limit and the lower limit of a class is called :
