### Understanding Relative Frequency HistogramsIn this section, we will explore the concept of relative frequency histograms and their interpretation through a specific example.#### Histogram Interpretation Example*Based on the relative frequency histogram below, which of the following statements is correct?*[Image of Relative Frequency Histogram]**Histogram Details:**- **X-Axis (Horizontal):** Ranges from 0 to 40, representing the data values.- **Y-Axis (Vertical):** Ranges from 0 to 0.4, representing the relative frequency of the data values.- The histogram contains several bars of varying heights that represent different ranges of data. - The tallest bar is located in the range of 5 to 10 with a relative frequency peak at approximately 0.35.#### Explanation of the Options:1. **The IQR of the distribution is about 10.** - **IQR (Interquartile Range)** is a measure of statistical dispersion and indicates the range within which the middle 50% of the data lie. It is difficult to precisely determine the IQR from only the histogram without additional data points.2. **The distribution is multimodal.** - **Multimodality** indicates the presence of multiple peaks or modes in the data. Observing the histogram, there is more than one peak at various intervals, making this option correct.3. **It is not possible to estimate the median without knowing the sample size.** - **Median Estimation** typically does require knowledge of the sample size, but in this context, it can be inferred from the histogram's data distribution.4. **The mean of the distribution is smaller than its median.** - **Mean vs. Median** examines the central tendency of the data. The histogram's skewness could suggest whether the mean is smaller than the median; however, further calculation or more data is usually needed for confirmation.5. **There are no outliers in the distribution.** - **Outliers** are data points significantly different from others in the dataset. While the histogram appears to have some bars at the tail end, a definitive conclusion regarding outliers requires further statistical analysis.**Correct Answer:**- The distribution is multimodal.This instance emphasizes the importance of correctly interpreting histograms to understand the underlying data distribution efficiently.

A bimodal distribution is the one in which we have two modes but in our graph, we see only one cleat…

Based on the relative frequency histogram below, which of the following statements is correct? 0.4 0.3 0.2 0.1 10 20 30 40 O The IQR of the distribution is about 10. The distribution is multimodal. O It is not possible to estimate the median without knowing the sample size. O The mean of the distribution is smaller than its median. O There are no outliers in the distribution. relative frequency

Based on the relative frequency histogram below, which of the following statements is correct? 0.4 0.3 0.2 0.1 10 20 30 40 O The IQR of the distribution is about 10. The distribution is multimodal. O It is not possible to estimate the median without knowing the sample size. O The mean of the distribution is smaller than its median. O There are no outliers in the distribution. relative frequency

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

### Understanding Relative Frequency Histograms

In this section, we will explore the concept of relative frequency histograms and their interpretation through a specific example.

#### Histogram Interpretation Example

*Based on the relative frequency histogram below, which of the following statements is correct?*

[Image of Relative Frequency Histogram]

**Histogram Details:**
- **X-Axis (Horizontal):** Ranges from 0 to 40, representing the data values.
- **Y-Axis (Vertical):** Ranges from 0 to 0.4, representing the relative frequency of the data values.
- The histogram contains several bars of varying heights that represent different ranges of data.
- The tallest bar is located in the range of 5 to 10 with a relative frequency peak at approximately 0.35.

#### Explanation of the Options:

1. **The IQR of the distribution is about 10.**
- **IQR (Interquartile Range)** is a measure of statistical dispersion and indicates the range within which the middle 50% of the data lie. It is difficult to precisely determine the IQR from only the histogram without additional data points.

2. **The distribution is multimodal.**
- **Multimodality** indicates the presence of multiple peaks or modes in the data. Observing the histogram, there is more than one peak at various intervals, making this option correct.

3. **It is not possible to estimate the median without knowing the sample size.**
- **Median Estimation** typically does require knowledge of the sample size, but in this context, it can be inferred from the histogram's data distribution.

4. **The mean of the distribution is smaller than its median.**
- **Mean vs. Median** examines the central tendency of the data. The histogram's skewness could suggest whether the mean is smaller than the median; however, further calculation or more data is usually needed for confirmation.

5. **There are no outliers in the distribution.**
- **Outliers** are data points significantly different from others in the dataset. While the histogram appears to have some bars at the tail end, a definitive conclusion regarding outliers requires further statistical analysis.

**Correct Answer:**
- The distribution is multimodal.

This instance emphasizes the importance of correctly interpreting histograms to understand the underlying data distribution efficiently.

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