Let's go through the process step by step to calculate the required statistical measures for the data given.
### Data Set
The data for the number of dogs adopted each day over three weeks (21 days) is:
[tex]\[ 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9 \][/tex]
### Mean (Average)
The mean is calculated by dividing the sum of all values by the number of values.
1. Sum of all values:
[tex]\[ 3 + 3 + 4 + 4 + 4 + 5 + 5 + 6 + 6 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 8 + 8 + 8 + 9 + 9 = 124 \][/tex]
2. Number of values:
There are 21 values in the data set.
3. Mean:
[tex]\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{124}{21} \approx 5.90 \][/tex]
So, the mean number of dogs adopted is approximately [tex]\( 5.90 \)[/tex].
### Median
The median is the middle value in an ordered data set. Since we have an odd number of observations (21), the median is the 11th value when the data is ordered.
The ordered data set is:
[tex]\[ 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, \boxed{7}, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9 \][/tex]
The 11th value is [tex]\( 7 \)[/tex].
So, the median number of dogs adopted is [tex]\( 7 \)[/tex].
### Mode
The mode is the number that appears most frequently in the data set.
In the given data set, the number [tex]\( 8 \)[/tex] appears the most frequently (5 times).
So, the mode is [tex]\( 8 \)[/tex].
### Range
The range is the difference between the highest and lowest values in the data set.
1. Lowest value: [tex]\( 3 \)[/tex]
2. Highest value: [tex]\( 9 \)[/tex]
3. Range:
[tex]\[ \text{Range} = \text{Highest value} - \text{Lowest value} = 9 - 3 = 6 \][/tex]
So, the range is [tex]\( 6 \)[/tex].
### Summary
- Mean: [tex]\( \approx 5.90 \)[/tex]
- Median: [tex]\( 7 \)[/tex]
- Mode: [tex]\( 8 \)[/tex]
- Range: [tex]\( 6 \)[/tex]
