SOLUTION: 1. An investigator decided to construct a frequency distribution with five classes. The following information was available. For fifty observations made on a characteristic under

Question 1205257: 1. An investigator decided to construct a frequency distribution with five classes. The following
information was available. For fifty observations made on a characteristic under study, the
first two and the last two frequencies were 6,10,10 and 6 respectively. Given the last class
mark is 66 and upper class limit of the fifth class is 72.
a. Calculate mean, Median and mode.
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
## Understanding the Problem
We have a frequency distribution with 5 classes and total observations = 50.
* First two class frequencies: 6, 10
* Last two class frequencies: 10, 6
* Last class mark: 66
* Upper limit of the last class: 72
## Constructing the Frequency Distribution Table
| Class Interval | Frequency (f) | Class Mark (x) | fx |
|---|---|---|---|
| | 6 | | |
| | 10 | | |
| | | | |
| | 10 | | |
| 66-72 | 6 | 69 | 414 |
## Finding Missing Values
1. **Class Width:**
* Class width = (Upper limit of last class - Lower limit of first class) / Number of classes
* Class width = (72 - Lower limit of first class) / 5
* We need to find the lower limit of the first class.
2. **Class Marks:**
* Class mark = (Upper limit + Lower limit) / 2
3. **Missing Frequencies:**
* Total frequency = 50
* Missing frequency = 50 - (6+10+10+6) = 18
## Completing the Table
Once we have the class width and missing frequency, we can complete the table. However, we still need more information to determine the exact class intervals and class marks.
**To proceed, we need either:**
1. **Lower limit of the first class:** This will allow us to calculate the class width and determine all class intervals and class marks.
2. **Class width:** This will allow us to determine the class intervals and class marks.
**Without this additional information, we cannot accurately calculate the mean, median, and mode.**
## Calculating Mean, Median, and Mode
Once we have the completed frequency distribution table, we can calculate these measures:
### Mean
* **Formula:** Mean = Σ(fx) / Σf
* Calculate Σfx by multiplying the frequency and class mark for each class, then summing these products.
* Divide Σfx by the total frequency (50).
### Median
* **Find the median class:** The median class is the class containing the 25th observation (halfway through the 50 observations).
* **Use the formula:** Median = L + [(N/2 - cf)/f] * h
* L = Lower limit of the median class
* N = Total frequency
* cf = Cumulative frequency of the class preceding the median class
* f = Frequency of the median class
* h = Class width
### Mode
* The mode is the class with the highest frequency.

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