Let's calculate the mean, median, and mode for the given data set: 22, 15, 49, 26, 42, 19, 27, 24.

1. Mean

The mean is calculated by summing all the values and then dividing by the number of values.

$\text{Mean} = \frac{22 + 15 + 49 + 26 + 42 + 19 + 27 + 24}{8} = \frac{224}{8} = 28.0$

2. Median

The median is the middle value when the data is sorted in ascending order. If the number of values is even, the median is the average of the two middle values.

• Sorted Data: 15, 19, 22, 24, 26, 27, 42, 49
• Since there are 8 values (even number), the median is the average of the 4th and 5th values: 24 and 26.

$\text{Median} = \frac{24 + 26}{2} = \frac{50}{2} = 25$

3. Mode

The mode is the value(s) that occur most frequently in the data set. If no value repeats, the mode does not exist (DNE).

• Each number in this set appears exactly once, so there is no mode.

$\text{Mode} = \text{DNE}$

Final Answers:

• Mean: 28.0
• Median: 25
• Mode: DNE

Would you like any details on these calculations, or have any questions?

Related Questions:

1. What is the range of the given data set?
2. How would the mode change if an additional 24 were added?
3. If the largest value (49) were removed, what would the new mean be?
4. What is the effect of adding 10 to each value on the mean, median, and mode?
5. If a new value, 15, were added, what would the new median be?

Tip: When calculating the median for an even number of values, always double-check the middle positions.