Statistics

Step 1: Define the statistical terms given in the options.
- (1) Range: In statistics, the range of a set of data is the difference between the largest and smallest values.
It is a simple measure of statistical dispersion or spread.
- (2) Mode: The value that appears most frequently in a data set.
It is a measure of central tendency.
- (3) Median: The middle value in a data set that has been arranged in order of magnitude.
It is a measure of central tendency.
- (4) Lorenz Curve: A graphical representation of the distribution of income or wealth.
It plots the cumulative percentage of total income received against the cumulative percentage of recipients, starting with the poorest individuals or households.
It is used to represent income inequality.

Step 2: Match the definition with the given description.
The description "The difference between the value of the smallest item and the value of the largest item" directly defines the Range.

Step 3: Confirm the correct term.
The range is calculated as: Range = Largest Value - Smallest Value.
This matches option (1).

Step 1: Define the statistical terms given in the options.
- (1) Range: In statistics, the range of a set of data is the difference between the largest and smallest values.
It is a simple measure of statistical dispersion or spread.
- (2) Mode: The value that appears most frequently in a data set.
It is a measure of central tendency.
- (3) Median: The middle value in a data set that has been arranged in order of magnitude.
It is a measure of central tendency.
- (4) Lorenz Curve: A graphical representation of the distribution of income or wealth.
It plots the cumulative percentage of total income received against the cumulative percentage of recipients, starting with the poorest individuals or households.
It is used to represent income inequality.

Step 2: Match the definition with the given description.
The description "The difference between the value of the smallest item and the value of the largest item" directly defines the Range.

Step 3: Confirm the correct term.
The range is calculated as: Range = Largest Value - Smallest Value.
This matches option (1).

Step 1: Define the statistical terms.
- Arithmetic Mean (Average): The sum of all values divided by the number of values.
- Median: The middle value in a dataset that has been arranged in order of magnitude.
If there is an even number of observations, the median is the average of the two middle values.
- Mode: The value that appears most frequently in a dataset.
A dataset can have one mode (unimodal), more than one mode (bimodal, multimodal), or no mode if all values occur with the same frequency.
- Range: The difference between the highest and lowest values in a dataset.
It is a measure of dispersion, not central tendency.

Step 2: Match the definition with "most frequently observed value".
The definition of Mode is the value that occurs most frequently in a data set.
This matches option (3).

Step 1: Identify the terms in the formula for the mode of grouped data.
The formula for calculating the mode of a continuous grouped frequency distribution is: where: - = lower limit of the modal class.
- = size of the class interval (assuming all class sizes are equal).
- = frequency of the modal class (the class with the highest frequency).
- = frequency of the class preceding the modal class.
- = frequency of the class succeeding the modal class.

Step 2: Match with its definition.
According to the standard definition of the terms in this formula, represents the frequency of the modal class.
This matches option (1).

Step 1: Understand the definition of a class mark.
In statistics, for a grouped frequency distribution, a class interval has a lower limit and an upper limit.
The class mark (or midpoint) of a class interval is the value that represents the center of that interval.
It is used in calculations like finding the mean of grouped data.

Step 2: Recall the formula for the class mark.
The class mark is calculated as the average of the upper and lower limits of the class interval.
Or, equivalently,
Step 3: Compare with the given options.
Option (1) matches this formula.
Option (2) represents half the class size or range, not the midpoint.
Options (3) and (4) are incorrect operations for finding a midpoint.
(The OCR for option (4) in the Telugu part shows Upperlimit+lowerlimit / 2 which is same as (1).
However, English option shows division, which is clearly wrong).
Assuming the English options are to be followed, option (1) is correct.