https://file.aiquickdraw.com/mathbot/file/17264319146984nb592kr.jpg

The expression in the image is:

\[
\frac{(1.44 - 1.484)^2 + (1.49 - 1.484)^2 + (1.55 - 1.484)^2 + (1.35 - 1.484)^2 + (1.59 - 1.484)^2}{5 - 1}
\]

Let me break it down and solve it step by step:

### Step 1: Simplify each term in the numerator
- \( 1.44 - 1.484 = -0.044 \)
- \( 1.49 - 1.484 = 0.006 \)
- \( 1.55 - 1.484 = 0.066 \)
- \( 1.35 - 1.484 = -0.134 \)
- \( 1.59 - 1.484 = 0.106 \)

### Step 2: Square each difference
- \( (-0.044)^2 = 0.001936 \)
- \( (0.006)^2 = 0.000036 \)
- \( (0.066)^2 = 0.004356 \)
- \( (-0.134)^2 = 0.017956 \)
- \( (0.106)^2 = 0.011236 \)

### Step 3: Sum the squared differences
\[
0.001936 + 0.000036 + 0.004356 + 0.017956 + 0.011236 = 0.03552
\]

### Step 4: Divide by the denominator \( 5 - 1 = 4 \)
\[
\frac{0.03552}{4} = 0.00888
\]

So, the result is approximately \( 0.00888 \).

Would you like any further explanation, or is there another part you'd like to focus on?

Here are 5 related questions you might explore:
1. How does this calculation relate to variance or standard deviation?
2. What is the significance of squaring the differences in this type of calculation?
3. Can this method be applied to larger datasets, and how does it scale?
4. What are some other statistical applications of this formula?
5. How does this formula connect to the concept of "mean" in statistics?

**Tip**: This is an example of finding the sample variance, which measures how much the data points differ from the mean.

Calculate the sample variance for the data set: {1.44, 1.49, 1.55, 1.35, 1.59}, with the mean 1.484.

Learn how to calculate the sample variance for the data set {1.44, 1.49, 1.55, 1.35, 1.59} with a mean of 1.484. Follow a step-by-step guide using the sample variance formula to compute the result, suitable for Grades 10-12.

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