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Chapter 25: Problem 1

The median of the numbers \(11,10,12,13,9\) is (a) \(12.5\) (b) 12 (c) \(10.5\) (d) 11 .

Short Answer

Expert verified
The median is 11.

Step by step solution

01

Arrange the Numbers

List the numbers in ascending order: 9, 10, 11, 12, 13. Arranging the numbers is the first step to finding the median.
02

Find the Middle Number

Look at the list of numbers you arranged in Step 1: 9, 10, 11, 12, 13. Because there are 5 numbers, the median is the middle number. In this list, the middle number is 11.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Arranging Numbers
To find the median, the first thing we need to do is organize the numbers we have. This process is known as arranging numbers, and it serves as a crucial step in many statistical calculations.

Imagine if we had a deck of cards spread out on a table; it would be much easier to find a specific card if they were sorted in order. Similarly, arranging numbers allows us to see the numbers in a neat sequence. There are different ways to arrange numbers, but when dealing with statistics such as finding the median, we focus on a particular type of order.

Next, we'll discuss what type of order is most helpful.
Ascending Order
When we arrange numbers for statistical purposes, such as finding the median, we usually put them in ascending order. This means the numbers are listed from the smallest to the largest.
  • Smallest numbers come first.
  • Larger numbers follow in sequence.
For example, if you have the numbers 11, 10, 12, 13, and 9, you would start with the smallest number, 9, and continue until you reach the largest number, 13.

Arranging the numbers as 9, 10, 11, 12, 13 simplifies the process of identifying relationships such as the median. By seeing the numbers in this logical sequence, you can easily pinpoint the next key concept: the middle number.
Middle Number
After arranging numbers in ascending order, the next step in finding the median is identifying the middle number.

The middle number is exactly what it sounds like: it's the number that sits right in the center of the row of numbers. To determine the middle number, especially when the count of numbers is odd, count equally from both ends until you meet in the middle.
  • If you have 5 numbers, the middle number is the third number in that ordered list.
  • For the list 9, 10, 11, 12, 13, the middle number鈥攁nd hence the median鈥攊s 11.
Understanding the concept of the middle number helps greatly in determining central tendency in a set of numbers.
Statistics
Statistics is a branch of mathematics that deals with data collection, analysis, interpretation, and presentation. Within statistics, the median is a measure of central tendency.

Central tendency helps us understand a set of data by summarizing it with a single value which represents the "center" of the data. Aside from the median, other measures of central tendency include the mean and mode. But unlike the mean, the median is less affected by extreme values (outliers).
  • The median gives a more reliable central value when compared to the mean in a skewed distribution.
  • It's particularly useful in real-world applications, such as household income, where extreme values can skew the mean.
In summary, by finding the median, we can gain insights about our data without being misled by unusually high or low values.

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Most popular questions from this chapter

The minimum value of correlation coefficient is \(\ldots \ldots .\)

The equations of regresuion lines are \(y=0.5 x+a\) and \(x=0.4 y+b\), The correlation coefficient is (a) \(\sqrt{0.2}\) (b) \(0.46\) (c) \(-\sqrt{0.2}\).

If \(X\) and \(Y\) are independent, then the correlation coefficient between \(X\) and \(Y\) is ........

Regression coefficient of \(y\) on \(x\) is \(0.7\) and that of \(x\) on \(y\) is 3.2. Is the correlntion coefficient \(r\) consistent ?

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