What is the major assumption we make when computing a mean form Grouped data:

Correct option is B

When calculating the mean from grouped data, we assume that all values within a given class interval are evenly distributed and can be represented by the midpoint of that class.

Why do we use the midpoint?

• Grouped data presents values in class intervals rather than individual observations.

• Since we do not know the exact values within each interval, we take the midpoint (class mark) as the representative value.

• The midpoint of a class interval is calculated as:
  Midpoint = (Lower Bound + Upper Bound) ÷ 2

• This assumption simplifies the calculation of the mean using the formula:

  Mean = (Σ f × Midpoint) ÷ Σ f

  where:

  • f = frequency of each class

  • Midpoint = representative value of each class

  • Σ f = total frequency

By assuming that all data points in a class are concentrated at the midpoint, we estimate the mean efficiently without needing the actual data values.

Information Booster:

1. Grouped data is data categorized into class intervals instead of individual values.

2. The midpoint assumption helps in estimating the mean when we do not have precise values.

3. The mean formula for grouped data is:

   Mean = (Sum of (Midpoint × Frequency)) ÷ Total Frequency

4. Limitations of the assumption:

   • The actual data values may not be concentrated at the midpoint.

   • This method provides an approximation rather than an exact mean.

   • It is more accurate when the class intervals are small and evenly distributed.

Additional Knowledge:

(a) All values are discrete.
Incorrect:

• Grouped data can contain both discrete and continuous values.

• The assumption of midpoints applies to both discrete and continuous data.

• Mean calculation does not require all values to be discrete.

(c) Each class contains exactly the same number of values.
Incorrect:

• In real-world data, class intervals can have different frequencies (some intervals have more data points than others).

• The mean formula accounts for varying frequencies of different class intervals.

(d) No value occurs more than once.
Incorrect:

• Repetition of values does not affect the assumption of midpoints.

• Some values may appear multiple times in the dataset, but we still estimate the mean using class midpoints.