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Answer :
To find the median of the data set
$$93,\ 81,\ 94,\ 71,\ 89,\ 92,\ 94,\ 99,$$
follow these steps:
1. **Sort the Data:**
Arrange the numbers in ascending order. The sorted list is
$$71,\ 81,\ 89,\ 92,\ 93,\ 94,\ 94,\ 99.$$
2. **Count the Number of Data Points:**
There are $8$ numbers in total.
3. **Determine the Position of the Middle Values:**
Since the number of data points is even, the median is the average of the two middle numbers. For a list of $8$ elements, the two middle positions are given by:
$$\text{Middle indices: } \frac{8}{2} = 4 \quad \text{and} \quad \frac{8}{2} - 1 = 3.$$
In the sorted list, the element in the $4^{\text{th}}$ position is $92$ and the element in the $5^{\text{th}}$ position is $93$.
4. **Calculate the Median:**
The median is computed by taking the average of these two middle values:
$$\text{Median} = \frac{92 + 93}{2} = \frac{185}{2} = 92.5.$$
Thus, the median of the given data is
$$\boxed{92.5}.$$
$$93,\ 81,\ 94,\ 71,\ 89,\ 92,\ 94,\ 99,$$
follow these steps:
1. **Sort the Data:**
Arrange the numbers in ascending order. The sorted list is
$$71,\ 81,\ 89,\ 92,\ 93,\ 94,\ 94,\ 99.$$
2. **Count the Number of Data Points:**
There are $8$ numbers in total.
3. **Determine the Position of the Middle Values:**
Since the number of data points is even, the median is the average of the two middle numbers. For a list of $8$ elements, the two middle positions are given by:
$$\text{Middle indices: } \frac{8}{2} = 4 \quad \text{and} \quad \frac{8}{2} - 1 = 3.$$
In the sorted list, the element in the $4^{\text{th}}$ position is $92$ and the element in the $5^{\text{th}}$ position is $93$.
4. **Calculate the Median:**
The median is computed by taking the average of these two middle values:
$$\text{Median} = \frac{92 + 93}{2} = \frac{185}{2} = 92.5.$$
Thus, the median of the given data is
$$\boxed{92.5}.$$
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