The image displays a problem where you are asked to compute statistical measures based on the temperature readings of 12 individuals. The temperature readings given are:

$38.2, 38.4, 38.7, 38.9, 38.5, 38.0, 38.4, 38.4, 38.9, 38.7, 38.5, 38.9.$

Provided Answers:

• Mean: 38.45
• Median: 38.45
• Mode: 38.4, 38.9
• Range: 1
• Variance: 0.11

Let's verify each of these:

1. Mean: $\text{Mean} = \frac{38.2 + 38.4 + 38.7 + 38.9 + 38.5 + 38.0 + 38.4 + 38.4 + 38.9 + 38.7 + 38.5 + 38.9}{12}$

   Let's calculate it.

2. Median: Since there are 12 numbers, the median will be the average of the 6th and 7th numbers when the data is sorted.

3. Mode: The mode is the number(s) that appear most frequently.

4. Range: The range is the difference between the highest and lowest values.

5. Variance: The variance is calculated using the formula: $\text{Variance} = \frac{1}{n} \sum_{i=1}^{n} (x_i - \text{Mean})^2$ where $x_i$ are the individual data points.

I'll go ahead and verify these calculations.Here are the correct statistical measures based on the given dataHere are the correct statistical measures based on the given

1. Mean: $38.54$ (approximately)
2. Median: $38.5$
3. Mode: $38.4$ (appears 3 times)
4. Range: $0.90$ (approximately)
5. Variance: $0.076$ (approximately)

Observations:

• The mean you provided as $38.45$ is slightly off from the correct value of approximately $38.54$.
• The median is slightly different as well, with the correct value being $38.5$.
• The mode listed in the image is partially correct. $38.4$ is a mode, but the value $38.9$ does not have as many occurrences as $38.4$, which is the true mode.
• The range should be $0.90$, not $1$.
• The variance provided as $0.11$ differs from the calculated value of approximately $0.076$.

Would you like further details or clarification on any of these points? Here are five related questions for further exploration:

1. How does changing a single data point affect the mean and variance?
2. Can a dataset have more than one mode? How would that affect the data's interpretation?
3. What are some common uses of variance in data analysis?
4. How is the standard deviation related to variance, and why is it often preferred?
5. What are some limitations of using the range as a measure of variability?

Tip: Always double-check your calculations, especially when dealing with datasets, as small errors can significantly affect your results.