Which is the best to be used if the choices are measurement of central location? Values: 101 105 109 104 98 91 109 95 105 776 94 105 102 96 97

To determine the best measure of central location for the given data, let's first explore the common measures of central location: **mean**, **median**, and **mode**.

Here are the values provided: 
\[ 101, 105, 109, 104, 98, 91, 109, 95, 105, 776, 94, 105, 102, 96, 97 \]

1. **Mean**: This is the arithmetic average of the values.
2. **Median**: This is the middle value when the data is ordered from least to greatest.
3. **Mode**: This is the most frequently occurring value(s).

### Mean Calculation
To calculate the mean, we add up all the values and then divide by the number of values. However, note that there seems to be an extreme value (776), which could significantly affect the mean.

### Median Calculation
To find the median, we sort the values and select the middle value.

### Mode Calculation
The mode is the value that appears most frequently.

Let me compute these values for you to determine the most appropriate measure.Here are the calculated measures of central location for the given dataHere are the calculated measures of central location for the given 

1. **Mean**: 145.8
2. **Median**: 102
3. **Mode**: 105 (most frequent value)

### Conclusion:
- The **mean** is significantly higher due to the extreme value (776), indicating that it is heavily influenced by this outlier. Hence, the mean might not represent the central tendency effectively for this dataset.
- The **median** (102) is not affected by outliers and gives a better central location for skewed data like this.
- The **mode** (105) represents the most common value, which might be useful in some contexts but does not provide a full picture of central location.

Thus, **median** is likely the best measure of central location in this case, as it is not influenced by the outlier.

Would you like more details on any of these calculations or insights? 

### Related Questions:
1. How do outliers affect the mean in datasets?
2. In which cases is the mode the most useful measure of central tendency?
3. What are some situations where the median might not be appropriate?
4. How can you detect and handle outliers in a dataset?
5. Why might someone choose the mean over the median or mode, despite the presence of outliers?

### Tip:
Always check for outliers when using the mean, as they can heavily skew your results!

Discover the best measure of central location for a dataset with outliers, including values 101, 105, 109, and an outlier of 776. Learn about mean, median, and mode, and why the median is often the most reliable choice in the presence of extreme values. Suitable for students in Grades 9-12.

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