https://file.aiquickdraw.com/mathbot/file/17294858475993hp9swno.jpg

To find the mean and median of the frequency distribution, we will use the following steps:

### (a) **Find the mean:**
The mean for a frequency distribution is calculated using the formula:

\[
\text{Mean} = \frac{\sum (f_i \cdot x_i)}{\sum f_i}
\]

Where:
- \( f_i \) is the frequency of each value.
- \( x_i \) is the value.
- \( \sum f_i \) is the sum of the frequencies.

Given:
\[
\begin{array}{|c|c|}
\hline
\text{Value (x)} & \text{Frequency (f)} \\
\hline
613 & 13 \\
532 & 5 \\
605 & 11 \\
588 & 14 \\
589 & 9 \\
598 & 4 \\
\hline
\end{array}
\]

Now we calculate the sum of \( f_i \cdot x_i \) for each value and the sum of frequencies:
\[
\begin{aligned}
613 \cdot 13 &= 7969 \\
532 \cdot 5 &= 2660 \\
605 \cdot 11 &= 6655 \\
588 \cdot 14 &= 8232 \\
589 \cdot 9 &= 5301 \\
598 \cdot 4 &= 2392 \\
\end{aligned}
\]

Adding these values together:
\[
7969 + 2660 + 6655 + 8232 + 5301 + 2392 = 33209
\]

The total frequency is:
\[
13 + 5 + 11 + 14 + 9 + 4 = 56
\]

Thus, the mean is:
\[
\text{Mean} = \frac{33209}{56} \approx 593.0
\]

This matches the result you already have in the image.

### (b) **Find the median:**
The median is the middle value when the data is arranged in order. For a frequency distribution, you need to find the cumulative frequencies and determine which value corresponds to the middle frequency.

1. List the cumulative frequencies:
\[
\begin{array}{|c|c|}
\hline
\text{Value (x)} & \text{Cumulative Frequency} \\
\hline
532 & 5 \\
588 & 5 + 14 = 19 \\
589 & 19 + 9 = 28 \\
598 & 28 + 4 = 32 \\
605 & 32 + 11 = 43 \\
613 & 43 + 13 = 56 \\
\hline
\end{array}
\]

2. The total frequency is 56, so the middle position is \( \frac{56}{2} = 28 \).

The median lies in the value corresponding to the cumulative frequency of 28, which is **589**.

---

Do you need more details on this, or have any questions?

Here are 5 relative questions to explore further:
1. How would you find the mode of the frequency distribution?
2. What are the advantages of using the median over the mean?
3. How would the calculations change if the distribution had an outlier value?
4. Can you explain how the cumulative frequency is used to determine the median?
5. How would you interpret the range of this frequency distribution?

**Tip**: When calculating the mean for frequency distributions, ensure you handle the multiplication of values by their respective frequencies carefully to avoid errors in summing.

Consider the frequency distribution to the right. Complete parts (a) through (c) below: (a) Find the mean of the frequency distribution (b) Find the median of the frequency distribution.

Learn how to calculate the mean and median of a frequency distribution. This problem involves determining the mean using Σ(f_i * x_i) / Σf_i and finding the median based on cumulative frequencies. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation