Arithmetic Mean

To solve the problem, we need to find the mode of the given data set. The mode is the number that appears most frequently in a data set.

1. Listing the Given Prices:
46, 25, 11, 73, 73, 59, 28, 25, 73, 30, 25, 8, 25, 80, 25

2. Counting the Frequencies:
- 25 appears 5 times
- 73 appears 3 times
- Others appear less frequently

3. Identifying the Mode:
The number with the highest frequency is 25.

Final Answer:
The mode of the prices is .

To solve the problem, we need to find the missing value of from a frequency distribution table, given that the arithmetic mean is .

1. Understanding the Formula for Arithmetic Mean:
The formula for the mean of a frequency distribution is:


where is frequency and is the corresponding value.

2. Using the Given Table:

Let’s organize the values:

3. Compute and :

First, compute known values of :

So,

4. Substituting into the Mean Formula:

Given , so:

5. Solving the Equation:

Cross-multiplying:

Subtract from both sides:

Subtract from both sides:

Divide both sides by 0.55:

Final Answer:
The missing value is .

To solve the problem, we need to determine which statistical measure cannot be found when no value in a set of ungrouped data is repeated.

1. Understanding the Mean:
The mean is the average of the data values and can be calculated by adding all the values and dividing by the number of values. It does not require any repeated values.
✓ Can be determined.

2. Understanding the Median:
The median is the middle value of the data when arranged in ascending order. It does not require repetition of values.
✓ Can be determined.

3. Understanding the Mode:
The mode is the value that appears most frequently in the data. If no value is repeated, there is no mode.
✗ Cannot be determined (or does not exist in this case).

4. Conclusion:
When no value is repeated in a data set, the mode cannot be determined.

Final Answer:
Mode