Suppose a data set consists of 27 numbers. 11 of them are -1, 11 of them are 0, 4 of them are 0.4 and 1 of them are 62.

Let's summarize the data set:

- 11 numbers are \( -1 \),
- 11 numbers are \( 0 \),
- 4 numbers are \( 0.4 \),
- 1 number is \( 62 \).

The total number of data points is \( 11 + 11 + 4 + 1 = 27 \), which matches the data set's size. Now, based on this, we can compute various statistics, such as the **mean**, **median**, and **mode**.

### 1. Mean
The mean is calculated by summing all the values and dividing by the total number of data points.

\[
\text{Mean} = \frac{\sum \text{all values}}{n}
\]

The sum of all values:
\[
\text{Sum} = (11 \times -1) + (11 \times 0) + (4 \times 0.4) + (1 \times 62)
\]
\[
= -11 + 0 + 1.6 + 62 = 52.6
\]

Now, calculate the mean:
\[
\text{Mean} = \frac{52.6}{27} \approx 1.948
\]

### 2. Median
To find the median, we need to order the numbers and find the middle value.

- There are 11 numbers of \( -1 \),
- Followed by 11 numbers of \( 0 \),
- Followed by 4 numbers of \( 0.4 \),
- Followed by 1 number of \( 62 \).

The data set in order:  
\( \{-1, -1, -1, ..., -1 \} \text{ (11 times)}, \{0, 0, ..., 0\} \text{ (11 times)}, \{0.4, 0.4, 0.4, 0.4\}, \{62\} \).

Since there are 27 numbers, the middle number is the \( 14^\text{th} \) number (as \( \frac{27+1}{2} = 14 \)).

- The first 11 numbers are \( -1 \), the next 11 are \( 0 \), so the \( 14^\text{th} \) number is \( 0 \).

Thus, the **median** is \( 0 \).

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

- \( -1 \) appears 11 times,
- \( 0 \) appears 11 times,
- \( 0.4 \) appears 4 times,
- \( 62 \) appears 1 time.

Both \( -1 \) and \( 0 \) occur most frequently, 11 times each, so there are two modes: \( -1 \) and \( 0 \).

Thus, the **modes** are \( -1 \) and \( 0 \).

### Summary:
- **Mean**: \( \approx 1.948 \),
- **Median**: \( 0 \),
- **Modes**: \( -1 \) and \( 0 \).

Would you like further details or to explore another aspect of this dataset?

Here are 5 related questions to expand on this information:
1. How would the mean change if the number \( 62 \) were replaced by a smaller number, like \( 10 \)?
2. What is the effect of the number \( 62 \) on the mean? Is it an outlier?
3. Can we calculate the range of the data set?
4. How would adding more values to the dataset affect the median?
5. How do we calculate the variance and standard deviation for this data set?

**Tip**: When dealing with extreme values (like \( 62 \)), always check if they significantly affect your average or other statistical measures.

Explore how to calculate the mean, median, and mode for a data set of 27 numbers. This set includes values of -1, 0, 0.4, and a large number like 62, showcasing the impact of outliers. Learn how these statistical measures are derived step-by-step.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation