A random sample of size twenty of a golfer’s scores are given:
39, 40, 40, 41, 39, 40, 44, 43, 40, 41, 40, 41, , 41,
42, 43, 40, 41, 41, 41, 43.
Compute the mean, sample variance and the sample standard deviation
for the sample of the golfer’s scores.

To compute the mean, sample variance, and sample standard deviation for the golfer's scores, we can follow these steps:

### Given Data
The scores are:
\[ 39, 40, 40, 41, 39, 40, 44, 43, 40, 41, 40, 41, 41, 42, 43, 40, 41, 41, 41, 43 \]

### Step 1: Calculate the Mean
The mean \(\bar{x}\) is calculated by summing all the scores and dividing by the number of scores.

\[
\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}
\]

Where \( n = 20 \) (the number of scores).

### Step 2: Calculate the Sample Variance
The sample variance \( s^2 \) is calculated using the formula:

\[
s^2 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n - 1}
\]

### Step 3: Calculate the Sample Standard Deviation
The sample standard deviation \( s \) is the square root of the sample variance:

\[
s = \sqrt{s^2}
\]

Let's calculate these values.### Results:
1. **Mean**: The mean of the golfer's scores is \( \bar{x} = 41.0 \).
2. **Sample Variance**: The sample variance of the scores is \( s^2 = 1.895 \) (rounded to three decimal places).
3. **Sample Standard Deviation**: The sample standard deviation of the scores is \( s = 1.376 \) (rounded to three decimal places).

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

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Here are 8 related questions to explore:

1. How would you calculate the population variance if this were the entire population of scores?
2. What is the significance of the sample variance in understanding the spread of the scores?
3. How does the sample standard deviation relate to the variability in the golfer's performance?
4. What would happen to the mean, variance, and standard deviation if an outlier score was included?
5. How does the choice of using sample variance versus population variance affect the results?
6. Can you explain the difference between standard deviation and variance?
7. How would the results change if the sample size were doubled?
8. How would you interpret the standard deviation in the context of a golfer’s performance?

**Tip:** When calculating sample variance and standard deviation, always remember to use \( n-1 \) (Bessel's correction) to get an unbiased estimate.

Learn how to compute the mean, sample variance, and sample standard deviation of a golfer's scores using a random sample of twenty scores. Includes step-by-step calculations and explanations.

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