Answer :
Sure! Let's work through each part of the question step-by-step to find the mean, median, and mode of the given data set.
### Data Set
The data set you have is:
[tex]\[ 65.8, 86.1, 86.1, 86.1, 75.6, 44.5, 69, 50.1, 60.3, 51.7 \][/tex]
### Step 1: Finding the Arithmetic Mean
The arithmetic mean is the average of all the numbers in the data set. To find it, add up all the numbers, then divide by the total number of numbers.
1. Add all the numbers together:
[tex]\[
65.8 + 86.1 + 86.1 + 86.1 + 75.6 + 44.5 + 69 + 50.1 + 60.3 + 51.7 = 675.3
\][/tex]
2. Divide the sum by the number of data points (10 in this case):
[tex]\[
\text{Arithmetic mean} = \frac{675.3}{10} = 67.53
\][/tex]
So, the arithmetic mean is 67.53.
### Step 2: Finding the Median
The median is the middle number in a sorted list of numbers. If the number of observations is odd, the median is the middle number. If it's even, the median is the average of the two middle numbers.
1. First, sort the data set:
[tex]\[ 44.5, 50.1, 51.7, 60.3, 65.8, 69, 75.6, 86.1, 86.1, 86.1 \][/tex]
2. Since there are 10 numbers, which is even, the median will be the average of the 5th and 6th numbers:
[tex]\[
\text{Median} = \frac{65.8 + 69}{2} = 67.4
\][/tex]
So, the median is 67.4.
### Step 3: Finding the Mode
The mode is the number that appears most frequently in the data set.
1. Count the frequency of each number:
- 86.1 appears 3 times
- All other numbers appear only once
The most frequently occurring number is 86.1.
So, the mode is 86.1.
Here are the final answers for the data set:
- Mean: 67.53
- Median: 67.4
- Mode: 86.1
### Data Set
The data set you have is:
[tex]\[ 65.8, 86.1, 86.1, 86.1, 75.6, 44.5, 69, 50.1, 60.3, 51.7 \][/tex]
### Step 1: Finding the Arithmetic Mean
The arithmetic mean is the average of all the numbers in the data set. To find it, add up all the numbers, then divide by the total number of numbers.
1. Add all the numbers together:
[tex]\[
65.8 + 86.1 + 86.1 + 86.1 + 75.6 + 44.5 + 69 + 50.1 + 60.3 + 51.7 = 675.3
\][/tex]
2. Divide the sum by the number of data points (10 in this case):
[tex]\[
\text{Arithmetic mean} = \frac{675.3}{10} = 67.53
\][/tex]
So, the arithmetic mean is 67.53.
### Step 2: Finding the Median
The median is the middle number in a sorted list of numbers. If the number of observations is odd, the median is the middle number. If it's even, the median is the average of the two middle numbers.
1. First, sort the data set:
[tex]\[ 44.5, 50.1, 51.7, 60.3, 65.8, 69, 75.6, 86.1, 86.1, 86.1 \][/tex]
2. Since there are 10 numbers, which is even, the median will be the average of the 5th and 6th numbers:
[tex]\[
\text{Median} = \frac{65.8 + 69}{2} = 67.4
\][/tex]
So, the median is 67.4.
### Step 3: Finding the Mode
The mode is the number that appears most frequently in the data set.
1. Count the frequency of each number:
- 86.1 appears 3 times
- All other numbers appear only once
The most frequently occurring number is 86.1.
So, the mode is 86.1.
Here are the final answers for the data set:
- Mean: 67.53
- Median: 67.4
- Mode: 86.1
