Find the range and the variance (correct to one decimal place).

77, 92, 93, 93, 98

(b) Find the variance =

I had the range correct except the variance.

What did you get, and how did you find it?

See also previous answer:

http://www.jiskha.com/display.cgi?id=1338606009

To find the variance for a set of numbers, you can follow these steps:

Step 1: Find the mean of the data set.
- Add up all the numbers in the data set: 77 + 92 + 93 + 93 + 98 = 453.
- Divide the sum by the number of data points: 453 / 5 = 90.6.

Step 2: Subtract the mean from each data point to find the deviation.
- Deviation of 77: 77 - 90.6 = -13.6
- Deviation of 92: 92 - 90.6 = 1.4
- Deviation of 93: 93 - 90.6 = 2.4
- Deviation of 93: 93 - 90.6 = 2.4
- Deviation of 98: 98 - 90.6 = 7.4

Step 3: Square each deviation.
- Squared deviation of -13.6: (-13.6)^2 ≈ 184.96
- Squared deviation of 1.4: (1.4)^2 = 1.96
- Squared deviation of 2.4: (2.4)^2 = 5.76
- Squared deviation of 2.4: (2.4)^2 = 5.76
- Squared deviation of 7.4: (7.4)^2 ≈ 54.76

Step 4: Find the average of the squared deviations.
- Add up all the squared deviations: 184.96 + 1.96 + 5.76 + 5.76 + 54.76 ≈ 253
- Divide the sum by the number of data points: 253 / 5 = 50.6.

The variance is approximately 50.6.

Now let's find the range of the data set:

Range is the difference between the maximum and minimum values in a data set.

In this case, the maximum value is 98 and the minimum value is 77.

Range = 98 - 77 = 21.

So, the range is 21 and the variance is 50.6.