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The abscissa of the point of intersection of the less than type and of the more than type ogives of a grouped data gives its
- a)mean
- b)mode
- c)median
- d)all the three
Correct answer is option 'C'. Can you explain this answer?
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The abscissa of the point of intersection of the less than type and of...
The question is asking about the abscissa (x-coordinate) of the point where the less than type and more than type ogives intersect in a grouped data.
To understand this concept, let's first define what an ogive is. An ogive is a graph that represents the cumulative frequency distribution of a dataset. It is used to visualize the cumulative frequencies at or below a certain value.
Now, let's break down the options given in the question and explain why the correct answer is option 'C' (median):
1. Mean: The mean is a measure of central tendency that represents the average value of a dataset. It is calculated by summing up all the values and dividing by the total number of values. The abscissa of the point of intersection of the ogives does not give us any information about the mean of the data, so option 'A' is incorrect.
2. Mode: The mode is the most frequently occurring value in a dataset. It is not related to the abscissa of the point of intersection of the ogives. Therefore, option 'B' is incorrect.
3. Median: The median is the middle value of a dataset when it is arranged in ascending or descending order. It is a measure of central tendency that divides the dataset into two equal halves. When we construct the ogives for a grouped data, the point where the less than type and more than type ogives intersect represents the median. This point corresponds to the cumulative frequency that is half of the total frequency. Therefore, option 'C' is correct.
4. All the three: Option 'D' is incorrect because the abscissa of the point of intersection of the ogives does not give any information about the mean or mode of the data.
In conclusion, the abscissa of the point of intersection of the less than type and more than type ogives in a grouped data gives the value of the median.
To understand this concept, let's first define what an ogive is. An ogive is a graph that represents the cumulative frequency distribution of a dataset. It is used to visualize the cumulative frequencies at or below a certain value.
Now, let's break down the options given in the question and explain why the correct answer is option 'C' (median):
1. Mean: The mean is a measure of central tendency that represents the average value of a dataset. It is calculated by summing up all the values and dividing by the total number of values. The abscissa of the point of intersection of the ogives does not give us any information about the mean of the data, so option 'A' is incorrect.
2. Mode: The mode is the most frequently occurring value in a dataset. It is not related to the abscissa of the point of intersection of the ogives. Therefore, option 'B' is incorrect.
3. Median: The median is the middle value of a dataset when it is arranged in ascending or descending order. It is a measure of central tendency that divides the dataset into two equal halves. When we construct the ogives for a grouped data, the point where the less than type and more than type ogives intersect represents the median. This point corresponds to the cumulative frequency that is half of the total frequency. Therefore, option 'C' is correct.
4. All the three: Option 'D' is incorrect because the abscissa of the point of intersection of the ogives does not give any information about the mean or mode of the data.
In conclusion, the abscissa of the point of intersection of the less than type and more than type ogives in a grouped data gives the value of the median.
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