Definitions [5]
Frequency Distribution Table: When the number of observations in an experiment is large then we can convert it into the tabular form which is called a Frequency Distribution Table.
Ungrouped Frequency Distribution Table: When the frequency of each class interval is not arranged or organized in any manner.
Grouped Frequency Distribution Table: The frequencies of the corresponding class intervals are organised or arranged in a particular manner, either ascending or descending.
Inclusive or discontinuous Frequency Distribution: A frequency distribution in which the upper limit of one class differs from the lower limit of the succeeding class is called an Inclusive or discontinuous Frequency Distribution.
Exclusive or continuous Frequency Distribution: A frequency distribution in which the upper limit of one class coincides from the lower limit of the succeeding class is called an exclusive or continuous Frequency Distribution.
Answer the following question in about 30 words:
Define the mean.
The mean is the value that is derived by summing all the values and dividing it by the number of observations.
`bar"x" = "Sum of observations"/"No. of observations"`
The arithmetic mean (or, simply, mean) of a set of numbers is obtained by dividing the sum of the numbers in the set by the number of numbers.
\[\mathbf{Mean}=\frac{\left(x_1+x_2+x_3+\ldots+x_n\right)}{n}=\frac{\Sigma x_i}{n}\]
Median is the value of the middle-most observation(s). The median is a measure of central tendency which gives the value of the middle-most observation in the data.
The mode is the value of the observation that occurs most frequently; i.e., the observation with the maximum frequency is called the mode.
Formulae [2]
If the number of data points (n) is odd, the median is,
Median = `((n+1)/2)^(th)` term
If n is even, the median is the average of the values at positions
Median = Average of `(n/2)^(th)` and `(n/2+1)^(th)` values
Key Points
- Grouped data uses class intervals.
- Class mark \[ x_{i} = \frac{\text{lower limit} + \text{upper limit}}{2}. \]
- Direct method: \[ \bar{x} = \frac{\sum f_{i}x_{i}}{N}. \]
- Assumed mean method: \[ \bar{x} = A + \frac{\sum f_{i}d_{i}}{N}. \]
- Step-deviation method: \[ \bar{x} = A + \left(\frac{\sum f_{i}u_{i}}{N}\right)g. \]
- \[ d_{i} = x_{i} - A, \; u_{i} = \frac{d_{i}}{g}, \; N = \sum f_{i}. \]
- The mean of grouped data is an estimate.
- Always show the calculation table and mention units in board answers.
Concepts [8]
- Frequency Distribution Table
- Measures of Central Tendency for Different Data Types
- Arithmetic Mean
- Mean of Grouped Data
- A Special Property of the Arithmetic Mean
- Basic Concept of Median
- Basic Concept of Mode
- Empirical Relationship Between the Three Measures of Central Tendency
