Question

The lower quartile of the data \(5,3,4,6,7,11,9\) is (1) 4 (2) 3 (3) 5 (4) 6

Short answer

A) 4 B) 5 C) 6 D) 3 Answer: A) 4

Step-by-step solution

Sort the data

Arrange the given data in ascending order: \(3, 4, 5, 6, 7, 9, 11\).

Find the median

The median of the data is the middle value. With 7 values in the data set, the median will be the 4th value, which is 6.

Find the lower quartile

The lower quartile is the median of the lower half of the data. Since our lower half is \(3, 4, 5\), the lower quartile will be the middle value of these numbers, which is 4.

Compare to choices

Comparing our answer to the given choices, we see that the lower quartile (4) matches choice (1). Hence, the correct answer is (1) 4.

Key concepts

Data Analysis

Data analysis is the process of inspecting and organizing data with the objective of discovering useful information. It plays a crucial role in interpreting complex data sets. In statistics, it's the first step to understanding and summarizing your data.

When approaching data analysis, one begins by gathering and arranging data. This might include categorizing or ranking the numbers for better clarity. Once organized, statistical methods, like finding quartiles or the median, help in deducing insightful inferences from the data.

• It provides a clearer picture and deeper insights into datasets.
• Helps in making data-driven decisions.
• Facilitates forecasting and predicting future trends.

Thus, adequate data analysis is foundational for meaningful statistical interpretations.

Median

The median is a measure of central tendency that reflects the middle value of a dataset when it is ordered. It's especially useful in understanding the distribution of the values as it divides the dataset into two equal halves. Whenever you have an odd number of data points, finding the median is straightforward. You simply pick the middle value.

For example, in a dataset like \(3, 4, 5, 6, 7, 9, 11\), after ordering, the median becomes the fourth number: \(6\). If the dataset has an even number of values, the median will be the average of the two middle numbers.

• Helps identify the center point in a dataset.
• Minimally affected by outliers, unlike the mean.
• Best suited for skewed data distributions.

The median is instrumental in statistical computations, ensuring you accurately interpret data.

Ordering Data

Ordering data is an essential task in the field of data analysis. It involves arranging the data points from the smallest to the largest. This step is critical because many statistical methods, like finding the median or quartiles, rely on properly ordered datasets.

Consider the dataset: \(5, 3, 4, 6, 7, 11, 9\). To process it correctly, first arrange these numbers as: \(3, 4, 5, 6, 7, 9, 11\). Now you can easily identify important key values like the median or the quartiles.

• Simplifies the process of finding specific statistical measures.
• Ensures that comparisons and interpretations are accurate.
• Maintains consistency in data analysis.

The ability to order data is a fundamental skill in statistics that facilitates deeper data insights.

Statistics for Class 8

Understanding statistics is vital for students, even as early as Class 8, as it lays the groundwork for higher-level mathematical concepts. Statistics deals with collecting, analyzing, interpreting, presenting, and organizing data.

In the context of Class 8, students learn basic statistical concepts such as the mean, median, mode, and how to find quartiles in datasets. These introduce young learners to practical math applications and equip them with necessary analytical skills.

• Provides foundational understanding of data-based patterns.
• Enhances mathematical reasoning and problem-solving skills.
• Prepares students for more advanced studies in mathematics and science.

By grasping these basics, Class 8 students gain valuable skills for academic advancement and real-world applications.