Problem Description:
The task involves finding the
median,
mode, and
range for a given set of numbers. The set of numbers provided is:
$$
12, 5, 9, 18, 22, 25, 5
$$
Step-by-Step Solution:
#### 1.
Organize the Data in Ascending Order
First, we need to arrange the numbers in ascending order to make it easier to calculate the median, mode, and range.
Given set:
$$
12, 5, 9, 18, 22, 25, 5
$$
Sorted set:
$$
5, 5, 9, 12, 18, 22, 25
$$
#### 2.
Calculate the Median
The
median is the middle value in an ordered list of numbers. If the list has an odd number of elements, the median is the middle element. If the list has an even number of elements, the median is the average of the two middle elements.
Here, the sorted list has 7 elements (an odd number), so the median is the 4th element.
Sorted list:
$$
5, 5, 9, 12, 18, 22, 25
$$
The 4th element is:
$$
\text{Median} = 12
$$
#### 3.
Calculate the Mode
The
mode is the number that appears most frequently in the list. If no number repeats, there is no mode. If multiple numbers have the same highest frequency, the data is multimodal.
From the sorted list:
$$
5, 5, 9, 12, 18, 22, 25
$$
The number
5 appears twice, which is more frequent than any other number.
$$
\text{Mode} = 5
$$
#### 4.
Calculate the Range
The
range is the difference between the largest and smallest values in the list.
From the sorted list:
$$
5, 5, 9, 12, 18, 22, 25
$$
The smallest value is:
$$
\text{Minimum} = 5
$$
The largest value is:
$$
\text{Maximum} = 25
$$
The range is:
$$
\text{Range} = \text{Maximum} - \text{Minimum} = 25 - 5 = 20
$$
Final Answers:
$$
\text{Median} = 12, \quad \text{Mode} = 5, \quad \text{Range} = 20
$$
Boxed Answer:
$$
\boxed{12, 5, 20}
$$
Parent Tip: Review the logic above to help your child master the concept of finding the mean median mode and range worksheet.
