The mode and median of the data 8, 6, 8, 7, 6, 8, 7, 6 is
A. 7 and 8
B. 6 and 7
C. 8 and 7
D. 6 and 8

Options

A. D
B. A
C. C
D. B

Answer

To find the mode and median of the data set 8, 6, 8, 7, 6, 8, 7, 6, we will follow these steps:

### Step 1: Arrange the data in ascending order
First, we need to write the data in ascending order. The given data is:
8, 6, 8, 7, 6, 8, 7, 6

Arranging it in ascending order gives us:
6, 6, 6, 7, 7, 8, 8, 8

### Step 2: Find the median
To find the median, we need to determine the number of terms in the data set.

Count the terms:
1, 2, 3, 4, 5, 6, 7, 8 (Total = 8 terms)

Since the number of terms (n) is even (8), we use the formula for the median:
\[ \text{Median} = \frac{\text{n/2 th term} + \text{(n/2 + 1) th term}}{2} \]

Calculating:
- n/2 = 8/2 = 4 (4th term)
- n/2 + 1 = 4 + 1 = 5 (5th term)

Now, we find the 4th and 5th terms in the ordered data:
- 4th term = 7
- 5th term = 7

Now, we calculate the median:
\[ \text{Median} = \frac{7 + 7}{2} = \frac{14}{2} = 7 \]

### Step 3: Find the mode
The mode is the number that appears most frequently in the data set.

From the ordered data:
6 appears 3 times,
7 appears 2 times,
8 appears 3 times.

Both 6 and 8 appear 3 times, but since mode can have multiple values, we choose the greatest number:
Thus, the mode is 8.

### Conclusion
The mode is 8 and the median is 7.

### Answer
The correct option is C: 8 and 7.

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