https://file.aiquickdraw.com/mathbot/file/173021607300401lwes1s.jpg

Let's go through each of these questions based on the data provided. I'll outline the steps needed to solve each question.

### 1. What is the class width?

To determine the class width:
- Find the range of the data by subtracting the minimum age from the maximum age.
- Divide this range by the number of classes (in this case, five) and round up to get the class width.

### 2. Construct a frequency distribution with five classes.

For this frequency distribution, we'll create five intervals (classes) based on the calculated class width. The columns should include:
- **Class limits** (the range of ages in each class)
- **Frequency** (the count of ages within each class)
- **Class midpoint** (average of the lower and upper class limits)
- **Relative frequency** (frequency divided by the total number of data points)
- **Cumulative frequency** (sum of frequencies up to each class)

### 3. Draw the histogram.

To draw a histogram:
- The x-axis will represent the age ranges (the five classes).
- The y-axis will represent the frequencies of each class.
- Plot the bars for each class based on the frequency data.

After creating the histogram, examine the shape of the distribution to determine if it appears symmetric, skewed left, or skewed right.

### 4. Calculate the mean, median, mode, standard deviation, and range of the age data.

1. **Mean**: Add up all the ages and divide by the total number of ages (46).
2. **Median**: Order the ages and find the middle value (or the average of the two middle values, since there is an even number of data points).
3. **Mode**: Identify the age or ages that occur most frequently.
4. **Standard deviation**: Use the formula for sample standard deviation:
   \[
   s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2}
   \]
5. **Range**: Subtract the minimum age from the maximum age.

### 5. Best measure of central tendency and why?

Based on the distribution's shape (symmetric or skewed), decide whether the **mean** or **median** best represents the central tendency of the data. The median is generally preferred if the data is skewed, as it is less affected by extreme values.

### 6. Calculate the five-number summary.

The five-number summary includes:
- **Minimum**: The smallest age in the dataset.
- **Q1 (First quartile)**: The median of the lower half of the data.
- **Median (Q2)**: The median of the entire data set.
- **Q3 (Third quartile)**: The median of the upper half of the data.
- **Maximum**: The largest age in the dataset.

### 7. Draw a box-and-whisker plot.

To create the box-and-whisker plot:
- Use the five-number summary to draw the box and whiskers.
- Determine if the plot suggests symmetry, left skew, or right skew based on the position of the median and the length of the whiskers.

---

Would you like to go through each of these calculations step-by-step, or is there a specific part of this problem you’d like help with first?

Construct a frequency distribution with five classes based on the ages of US Presidents at their first inauguration, and answer various statistical questions regarding the distribution.

Learn how to construct a frequency distribution of ages, calculate central tendencies, and create visualizations. This problem involves determining class width, constructing a frequency distribution table, and calculating mean, median, mode, and standard deviation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation