Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
Certainly! Let's break down the calculation for the mean, median, and mode of the given data.
### Data Set
```
52, 86, 76, 51, 62, 67, 70, 50,
45, 49, 54, 58, 53, 74, 64, 56,
50, 80, 10, 57, 64, 64, 43, 78,
84, 71, 55, 72, 78, 43, 42, 75,
84, 72, 69, 49, 66, 42, 65, 88
```
### 1. Mean
The mean (or average) is calculated by summing up all the values and dividing by the number of values.
Step-by-step calculation:
[tex]\[ \text{Sum} = 52 + 86 + 76 + 51 + 62 + 67 + 70 + 50 + 45 + 49 + 54 + 58 + 53 + 74 + 64 + 56 + 50 + 80 + 10 + 57 + 64 + 64 + 43 + 78 + 84 + 71 + 55 + 72 + 78 + 43 + 42 + 75 + 84 + 72 + 69 + 49 + 66 + 42 + 65 + 88 \][/tex]
Sum = 2744
We have 40 values in the dataset.
[tex]\[ \text{Mean} = \frac{\text{Sum}}{\text{Number of values}} = \frac{2744}{40} = 68.6 \][/tex]
### 2. Median
The median is the middle value in a sorted list of numbers. If the list has an even number of elements, the median is the average of the two middle numbers.
Step-by-step calculation:
First, sort the dataset:
[tex]\[ 10, 42, 42, 43, 43, 45, 49, 49, 50, 50, 52, 53, 54, 55, 56, 57, 58, 62, 64, 64, 64, 66, 67, 69, 70, 71, 72, 72, 74, 75, 76, 78, 78, 80, 84, 84, 84, 86, 88 \][/tex]
There are 40 values. The two middle values are the 20th and 21st values.
Middle two values are:
64 and 64
[tex]\[ \text{Median} = \frac{64 + 64}{2} = 64 \][/tex]
### 3. Mode
The mode is the value that appears most frequently in the dataset.
Step-by-step calculation:
Identifying the most frequent value(s) in the set:
- 64 appears 3 times
- 42 appears 3 times
- 43 appears 3 times
- 84 appears 3 times
- 78 appears 2 times
Since 64, 42, 43, and 84 occur the same highest number of times (i.e., three times each), there are multiple modes.
Therefore, the modes are: 42, 43, 64, and 84.
### Result Summary
- Mean: 68.6
- Median: 64
- Mode: 42, 43, 64, 84
### Data Set
```
52, 86, 76, 51, 62, 67, 70, 50,
45, 49, 54, 58, 53, 74, 64, 56,
50, 80, 10, 57, 64, 64, 43, 78,
84, 71, 55, 72, 78, 43, 42, 75,
84, 72, 69, 49, 66, 42, 65, 88
```
### 1. Mean
The mean (or average) is calculated by summing up all the values and dividing by the number of values.
Step-by-step calculation:
[tex]\[ \text{Sum} = 52 + 86 + 76 + 51 + 62 + 67 + 70 + 50 + 45 + 49 + 54 + 58 + 53 + 74 + 64 + 56 + 50 + 80 + 10 + 57 + 64 + 64 + 43 + 78 + 84 + 71 + 55 + 72 + 78 + 43 + 42 + 75 + 84 + 72 + 69 + 49 + 66 + 42 + 65 + 88 \][/tex]
Sum = 2744
We have 40 values in the dataset.
[tex]\[ \text{Mean} = \frac{\text{Sum}}{\text{Number of values}} = \frac{2744}{40} = 68.6 \][/tex]
### 2. Median
The median is the middle value in a sorted list of numbers. If the list has an even number of elements, the median is the average of the two middle numbers.
Step-by-step calculation:
First, sort the dataset:
[tex]\[ 10, 42, 42, 43, 43, 45, 49, 49, 50, 50, 52, 53, 54, 55, 56, 57, 58, 62, 64, 64, 64, 66, 67, 69, 70, 71, 72, 72, 74, 75, 76, 78, 78, 80, 84, 84, 84, 86, 88 \][/tex]
There are 40 values. The two middle values are the 20th and 21st values.
Middle two values are:
64 and 64
[tex]\[ \text{Median} = \frac{64 + 64}{2} = 64 \][/tex]
### 3. Mode
The mode is the value that appears most frequently in the dataset.
Step-by-step calculation:
Identifying the most frequent value(s) in the set:
- 64 appears 3 times
- 42 appears 3 times
- 43 appears 3 times
- 84 appears 3 times
- 78 appears 2 times
Since 64, 42, 43, and 84 occur the same highest number of times (i.e., three times each), there are multiple modes.
Therefore, the modes are: 42, 43, 64, and 84.
### Result Summary
- Mean: 68.6
- Median: 64
- Mode: 42, 43, 64, 84
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.