Question

Calculate the variance of the data 10,19,21,28,12,20,16 use demos Calculate graph

Answer 1

To calculate the variance of the data set \(10, 19, 21, 28, 12, 20, 16\), you can follow these steps:

### Step 1: Calculate the Mean

First, find the mean (average) of the data set.

\[
\text{Mean} = \frac{\sum \text{data points}}{N}
\]
where \(N\) is the number of data points.

\[
\text{Mean} = \frac{10 + 19 + 21 + 28 + 12 + 20 + 16}{7} = \frac{126}{7} = 18
\]

### Step 2: Calculate the Squared Differences from the Mean

Next, find the squared differences from the mean for each data point:

1. \( (10 - 18)^2 = (-8)^2 = 64 \)
2. \( (19 - 18)^2 = (1)^2 = 1 \)
3. \( (21 - 18)^2 = (3)^2 = 9 \)
4. \( (28 - 18)^2 = (10)^2 = 100 \)
5. \( (12 - 18)^2 = (-6)^2 = 36 \)
6. \( (20 - 18)^2 = (2)^2 = 4 \)
7. \( (16 - 18)^2 = (-2)^2 = 4 \)

### Step 3: Calculate the Variance

Now, find the variance using the formula:

\[
\text{Variance} = \frac{\sum \text{squared differences}}{N}
\]

Calculate the sum of squared differences:

\[
\sum \text{squared differences} = 64 + 1 + 9 + 100 + 36 + 4 + 4 = 218
\]

Finally, compute the variance:

\[
\text{Variance} = \frac{218}{7} \approx 31.14
\]

### Conclusion

The variance of the data set \(10, 19, 21, 28, 12, 20, 16\) is approximately \(31.14\).

### Graphical Representation

Since I can't create a graph directly in this environment, I can describe how you can visualize this:

1. **Bar Graph**: Create a bar graph with the data points \(10, 19, 21, 28, 12, 20, 16\) on the x-axis and their values on the y-axis. This gives a visual comparison of the data values.

2. **Scatter Plot**: You can plot each data point on a scatter plot to see how they are distributed.

3. **Box Plot**: A box plot can show the quartiles and give an idea of the spread and outliers.

To graph it yourself, use graphing software, Excel, or graph paper for manual plotting.