Certainly! Let's work through the calculations to determine the median and mode of the given data set.
### Data Set
The given data set is:
[tex]\[48, 25, 34, 46, 29, 27, 46\][/tex]
### Step-by-Step Calculation
#### Step 1: Calculate the Median
The median is the middle value of a data set when it is ordered from least to greatest.
1. First, we sort the data in ascending order:
[tex]\[25, 27, 29, 34, 46, 46, 48\][/tex]
2. Since there are 7 numbers in the data set (an odd number), the median is the fourth number in the ordered list:
[tex]\[ \text{Median} = 34 \][/tex]
#### Step 2: Calculate the Mode
The mode is the number that appears most frequently in the data set.
1. We observe the frequency of each number in the data set:
- 25: 1 time
- 27: 1 time
- 29: 1 time
- 34: 1 time
- 46: 2 times
- 48: 1 time
2. The number 46 appears most frequently (2 times). Hence:
[tex]\[ \text{Mode} = 46 \][/tex]
### Conclusion
Based on our calculations:
- The median is 34.
- The mode is 46.
Among the given choices:
a. median: 46, mode: 46
b. median: 34, mode: 36
c. median: 46, mode: 48
d. median: 34, mode: 46
The correct option that matches our calculated values is choice:
[tex]\[ \boxed{\text{d}} \][/tex]
