Cholesterol levels were collected from patients two days after they had a heart attack (Ryan, Joiner & Ryan, Jr, 1985). Retrieved from http://www.statsci.org/data/general/cholest.html.

Cholesterol Levels
270
236
210
142
280
272
160
220
226
242
186
266
206
318
294
282
234
224
276
282
360
310
280
278
288
288
244
236
Compute the variance. Round the answer to two decimal places.

To calculate the variance of the cholesterol levels, we follow these steps:

### Step 1: Calculate the mean (average)
The mean is calculated by summing all the cholesterol levels and then dividing by the number of data points.

Data points:
270, 236, 210, 142, 280, 272, 160, 220, 226, 242, 186, 266, 206, 318, 294, 282, 234, 224, 276, 282, 360, 310, 280, 278, 288, 288, 244, 236

### Step 2: Calculate each squared deviation from the mean
After finding the mean, for each data point, subtract the mean and square the result.

### Step 3: Calculate the variance
The variance is the average of these squared deviations. Since we're working with a sample, we divide by \(n-1\) (where \(n\) is the number of data points) to get the sample variance.

Let's calculate that now.

 numpy as np

# Cholesterol levels data
cholesterol_levels = [270, 236, 210, 142, 280, 272, 160, 220, 226, 242, 186, 266, 206, 318, 
                      294, 282, 234, 224, 276, 282, 360, 310, 280, 278, 288, 288, 244, 236]

# Calculate the mean
mean_cholesterol = np.mean(cholesterol_levels)

# Calculate the variance (sample variance, divide by n-1)
variance_cholesterol = np.var(cholesterol_levels, ddof=1)

# Round to 2 decimal places
variance_cholesterol_rounded = round(variance_cholesterol, 2)

variance_cholesterol_roundedThe variance of the cholesterol levels is **2276.29** (rounded to two decimal places).

Would you like more details or have any questions?

Here are some related questions to consider:

1. How does variance relate to standard deviation, and how can you calculate it from variance?
2. What does the high variance in cholesterol levels suggest about the data?
3. How can you interpret the results in a medical context, given that this is data from heart attack patients?
4. How might sample variance differ from population variance, and why do we use \(n-1\) in the formula for sample variance?
5. How can you calculate the mean and variance for data with missing values?

**Tip:** Variance gives a sense of the spread of data points from the mean. A higher variance means the data points are more spread out, while a lower variance indicates that the data points are closer to the mean.

Learn how to compute the variance of cholesterol levels collected from heart attack patients. This problem involves key statistical concepts such as variance calculation, descriptive statistics, and the sample variance theorem. The dataset includes cholesterol levels ranging from 142 to 360, with a final variance of 2276.29 (rounded to two decimal places).

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