In the United States, the Recording Industry Association of America (RIAA) awards artists with a platinum album certification when an album has sold one million copies. The following data set includes a random sample of five artists or groups along with the number of platinum albums in a recent year. Determine the sample variance, s2. Round your final answer to the nearest tenth if necessary.

**Random Sample of Artists or Groups with Platinum Albums**Artist or Group

Number of 

Platinum Albums

Alabama

49

The Rolling Stones

67

Eminem

62

U2

51

Neil Diamond

50


To determine the sample variance (\(s^2\)) for the number of platinum albums in the given sample of artists or groups, follow these steps:

### Step 1: List the Data
The data set includes the following values:

- Alabama: 49
- The Rolling Stones: 67
- Eminem: 62
- U2: 51
- Neil Diamond: 50

### Step 2: Calculate the Sample Mean (\(\bar{x}\))
The sample mean (\(\bar{x}\)) is the average number of platinum albums.

\[
\bar{x} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{49 + 67 + 62 + 51 + 50}{5}
\]

Let's calculate this:

\[
\bar{x} = \frac{49 + 67 + 62 + 51 + 50}{5} = \frac{279}{5} = 55.8
\]

### Step 3: Calculate Each Value's Deviation from the Mean and Square It
For each data point, subtract the mean and square the result:

\[
\text{Deviation for Alabama} = (49 - 55.8)^2 = (-6.8)^2 = 46.24
\]
\[
\text{Deviation for The Rolling Stones} = (67 - 55.8)^2 = (11.2)^2 = 125.44
\]
\[
\text{Deviation for Eminem} = (62 - 55.8)^2 = (6.2)^2 = 38.44
\]
\[
\text{Deviation for U2} = (51 - 55.8)^2 = (-4.8)^2 = 23.04
\]
\[
\text{Deviation for Neil Diamond} = (50 - 55.8)^2 = (-5.8)^2 = 33.64
\]

### Step 4: Calculate the Sample Variance (\(s^2\))
The sample variance is the sum of these squared deviations divided by the number of data points minus one (n-1):

\[
s^2 = \frac{46.24 + 125.44 + 38.44 + 23.04 + 33.64}{5 - 1} = \frac{266.8}{4} = 66.7
\]

### Final Answer
The sample variance (\(s^2\)) is **66.7** (rounded to the nearest tenth).

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Do you want details or have any questions?

Here are 5 related questions:
1. How is sample variance different from population variance?
2. Why do we divide by \(n-1\) instead of \(n\) when calculating sample variance?
3. Can you calculate the sample standard deviation from this variance?
4. What are some scenarios where sample variance is preferred over population variance?
5. How would adding another data point to this sample affect the variance?

**Tip:** In sample variance calculations, using \(n-1\) (the Bessel's correction) instead of \(n\) corrects for the bias that can occur when estimating the population variance from a small sample.

Learn how to calculate the sample variance (s^2) for a dataset of platinum albums by artists including Alabama, The Rolling Stones, Eminem, U2, and Neil Diamond. Understand the steps involved, including finding the mean, calculating deviations, and applying Bessel's correction. Suitable for high school students studying statistics.

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