Which one of the following pairs is correctly matched?
Median - Graphical location
Understanding Statistical Measures and Graphical Representation
This question asks us to identify the correctly matched pair between a statistical measure and a method of graphical location or representation. Let's examine each option to determine which statistical measure can be appropriately located or found using the specified graphical method.
Analyzing Each Option for Correct Matching
We will go through each given pair and evaluate its correctness:
- Median - Graphical location: The median is the middle value in a dataset when arranged in order. It divides the data into two equal halves. The median can indeed be found graphically using a cumulative frequency curve, also known as an ogive. By plotting the cumulative frequencies and drawing a line from the point corresponding to N/2 (where N is the total frequency) on the y-axis to the ogive and then down to the x-axis, we can locate the median. This process is a form of graphical location. Therefore, this pair is a potential correct match.
- Mean - Graphical location: The mean (arithmetic mean) is calculated by summing all values and dividing by the number of values. While graphical representations like histograms help visualize the data distribution, the mean itself is typically calculated mathematically and is not directly "located" on a graph in the same way as the median or mode. There isn't a standard graphical method to pinpoint the mean value directly from a chart like an ogive or histogram peak. Therefore, this pair is not correctly matched.
- Geometric mean - Ogive: The geometric mean is used for data that is averaged over time or represents rates of change. It is calculated using the nth root of the product of n values. An ogive, as discussed, is a cumulative frequency curve used to find values like quartiles, percentiles, and the median. The geometric mean cannot be found using an ogive. Therefore, this pair is not correctly matched.
- Mode - Ogive: The mode is the value that appears most frequently in a dataset. While the mode can be found graphically, the appropriate graph for locating the mode is a histogram, not an ogive. On a histogram, the mode is represented by the peak of the tallest bar. An ogive deals with cumulative frequencies and is not used to find the mode. Therefore, this pair is not correctly matched.
Based on the analysis of each option, the only pair where the statistical measure can be located or found using the specified graphical method is the first one: Median - Graphical location, specifically through the use of an ogive.
Summary of Graphical Methods for Statistical Measures
| Statistical Measure | Common Graphical Method for Location |
|---|---|
| Median | Ogive (Cumulative Frequency Curve) |
| Mode | Histogram |
| Mean | Calculated, not typically located graphically |
Thus, the pair "Median - Graphical location" correctly describes how the median can be determined using a graph, such as an ogive, which represents a graphical method for finding the median.
The correctly matched pair is Median - Graphical location.
Revision Table: Key Measures and Graphs
| Statistical Measure | Definition | Primary Graphical Tool for Location/Representation |
|---|---|---|
| Mean | Average value (sum of values / number of values) | Histogram (visualize distribution), not located directly |
| Median | Middle value in ordered data | Ogive (Cumulative Frequency Curve) |
| Mode | Most frequent value | Histogram |
| Geometric Mean | nth root of the product of n values | Calculated, not located graphically using standard methods |
Additional Information: Ogives and Cumulative Frequency
An ogive is a line graph that displays the cumulative frequency or cumulative relative frequency against the upper class boundaries of a frequency distribution. There are two types of ogives:
- Less than cumulative frequency ogive: Plots cumulative frequency against the upper limits of class intervals.
- More than cumulative frequency ogive: Plots cumulative frequency against the lower limits of class intervals.
The point where the 'less than' and 'more than' ogives intersect corresponds to the median on the x-axis. Alternatively, for a 'less than' ogive, the median is found by locating N/2 on the cumulative frequency axis (y-axis), drawing a horizontal line to the ogive, and then dropping a vertical line to the x-axis. The value on the x-axis is the median. This demonstrates the graphical location of the median using an ogive.
Similar Questions
If average weekly wages earned by a worker is Rs. 3,520, then what is the value of k?
What is the median (approximate value) of the distribution?
Which one of the following measures of central tendency will be used to determine the average size of the shoe sold in the shop?
If the mean of a set of 7 observations is 10 and the mean of a set of 3 observations is 5, then what is the combined mean?
The average weekly wages of male employees in a company is ₹4,200 and that of females is ₹3,200. If the average weekly wage of all employees is ₹4,000, what is the ratio of male to female employees?
Consider the observations x, x + 4, 30, 33, 74, 78, 49, 52, 98, 85. If the median of the data is 67, then what is the value of x?
A cyclist pedals from her house to her office at a speed of 3 kmph and back from the office to her house at 6 kmph. What is the average speed?
If the heights (in cm) of 9 students of a class are 150, 165, 145, 149, 150, 147, 152, 144 and 148, then what is the algebraic sum of the heights measured from their arithmetic mean?
Consider the following grouped data :
Class Frequency 0 – 10 4 10 – 20 8 20 – 30 15 30 – 40 10 40 – 50 3 What is the mode of the above distribution?
Consider the following incomplete frequency distribution with a total frequency of 100:
Class Frequency 0-10 10 10-20 x 20-30 20 30-40 y If the mean of the frequency distribution is 25, then what are the missing frequencies?
Important Questions from Measures of Central Tendency
A random sample of 20 people is classified in the following table according to their ages:
Age
Frequency
15 – 25
2
25 – 35
4
35 – 45
6
45 – 55
5
55 - 65
3
What is the mean age of this group of people?
The median of the following observations 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33 is 58. If 92 is replaced by 99 and 41 by 43 in the above data. The new median is:
If the difference of mode and median is 36, then the difference of median and mean is:
In a Mathematics test 15 students scored 80 marks, 20 students scored 75 marks, 28 students scored 65 marks and 25 students scored 60 marks, mode of the score is:
If the mode of the scores 10, 12, 13, 15, 15, 13, 12, 10, x is 15, then what is the value of x?
