1) Calculate the Mean, Median, Mode  for the following data set:

96,93,92,90,94, 93,91,90,95,92

Let's calculate the Mean, Median, and Mode for the given data set:

### Data Set:
\[96, 93, 92, 90, 94, 93, 91, 90, 95, 92\]

### 1. Mean:
The mean (average) is calculated by summing all the data points and then dividing by the number of data points.

\[
\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}} = \frac{96 + 93 + 92 + 90 + 94 + 93 + 91 + 90 + 95 + 92}{10} = \frac{936}{10} = 93.6
\]

### 2. Median:
The median is the middle value of the ordered data set. If there are an even number of observations, the median is the average of the two middle numbers.

First, let's order the data set:
\[90, 90, 91, 92, 92, 93, 93, 94, 95, 96\]

Since there are 10 data points (an even number), the median is the average of the 5th and 6th numbers:
\[
\text{Median} = \frac{92 + 93}{2} = \frac{185}{2} = 92.5
\]

### 3. Mode:
The mode is the number that appears most frequently in the data set.

In the ordered data set:
\[90, 90, 91, 92, 92, 93, 93, 94, 95, 96\]

- 90 appears twice
- 92 appears twice
- 93 appears twice

So, the data set has three modes (it's multimodal):
\[
\text{Mode} = 90, 92, 93
\]

### Summary:
- **Mean**: 93.6
- **Median**: 92.5
- **Mode**: 90, 92, 93

Would you like more details or have any questions?

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Here are 8 related questions you might find useful:

1. How would the mean change if a data point was added or removed?
2. How do you calculate the range of a data set?
3. What happens to the median if all data points are increased by the same amount?
4. How do you find the mode in a continuous data set?
5. What is the significance of the mode in a data set?
6. How does an outlier affect the mean, median, and mode?
7. What is the difference between a bimodal and a multimodal data set?
8. How would the calculations change if the data set had a large number of repeated values?

**Tip:** When calculating the median, always ensure the data set is ordered from smallest to largest before finding the middle value.

Learn how to calculate the mean, median, and mode for a given dataset. Step-by-step solution with examples. Suitable for high school students and anyone interested in statistical analysis.

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