Find the mean, median, and mode of the following data. If necessary, round to one more decimal place than the largest number of decimal places given in the data.

0.40
0.30
0.64
0.66
0.30
0.53
0.74
0.61
0.28
0.68
0.70
0.70
0.76
0.79
0.53
0.40
0.58
0.51
0.37
0.37

To find the **mean**, **median**, and **mode** of the given data, let's first organize the values and then calculate each of the statistical measures:

### Given Data (ordered):
0.28, 0.30, 0.30, 0.37, 0.37, 0.40, 0.40, 0.51, 0.53, 0.53, 0.58, 0.61, 0.64, 0.66, 0.68, 0.70, 0.70, 0.74, 0.76, 0.79

#### 1. **Mean**:
The mean is calculated by adding all the numbers and dividing by the total number of values.

\[
\text{Mean} = \frac{\sum x}{n}
\]

Where \( n = 20 \) is the total number of data points.

\[
\sum x = 0.28 + 0.30 + 0.30 + 0.37 + 0.37 + 0.40 + 0.40 + 0.51 + 0.53 + 0.53 + 0.58 + 0.61 + 0.64 + 0.66 + 0.68 + 0.70 + 0.70 + 0.74 + 0.76 + 0.79 = 11.56
\]

Now divide by 20:

\[
\text{Mean} = \frac{11.56}{20} = 0.578
\]

#### 2. **Median**:
The median is the middle value of an ordered dataset. Since we have 20 values (an even number), the median is the average of the 10th and 11th values.

The 10th value is 0.53, and the 11th value is 0.58.

\[
\text{Median} = \frac{0.53 + 0.58}{2} = \frac{1.11}{2} = 0.555
\]

#### 3. **Mode**:
The mode is the value that appears most frequently in the dataset. In this case, the value that appears most often is:

\[
\text{Mode} = 0.30 \quad \text{and} \quad 0.70 \quad (\text{both appear twice})
\]

Thus, the data is **bimodal**.

### Final Results:
- **Mean**: 0.578
- **Median**: 0.555
- **Mode**: 0.30, 0.70 (bimodal)

Would you like more details or have any questions? 

Here are 5 related questions you can explore:
1. How do outliers affect the mean, median, and mode?
2. What is the difference between a bimodal and a unimodal distribution?
3. What is the impact of rounding on statistical results?
4. How would you find the range and standard deviation for this data set?
5. How does the median change if we remove the highest and lowest values?

**Tip**: When data is skewed, the mean is affected more by extreme values than the median.

Learn how to calculate the mean, median, and mode of a given dataset including values like 0.40, 0.30, 0.64, and more. This detailed explanation is suitable for students in Grades 6-8 and covers essential statistical concepts such as measures of central tendency.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation