Find the range and the standard deviation (correct to two decimal places).

77, 89, 96, 96, 102

Range = max -min

Range =102 -77
Range = 25
Standard deviation = 8.56

To find the range and standard deviation of a set of numbers, you'll need to perform a few calculations.

Step 1: Find the range.
The range is simply the difference between the highest and lowest values in the set. In this case, the lowest value is 77 and the highest value is 102. So, the range is 102 - 77 = 25.

Step 2: Find the mean (average).
The mean is the sum of all values divided by the number of values. In this case, the sum of the values is 77 + 89 + 96 + 96 + 102 = 460. Since there are 5 values, the mean is 460 / 5 = 92.

Step 3: Find the deviation of each value from the mean.
To find the deviation of each value from the mean, subtract the mean from each individual value. In this case, the deviations are:

77 - 92 = -15
89 - 92 = -3
96 - 92 = 4
96 - 92 = 4
102 - 92 = 10

Step 4: Square each deviation and find the sum of the squared deviations.
Square each deviation and find the sum of the squared deviations. In this case, the squared deviations are:

(-15)^2 = 225
(-3)^2 = 9
4^2 = 16
4^2 = 16
10^2 = 100

The sum of the squared deviations is 225 + 9 + 16 + 16 + 100 = 366.

Step 5: Find the variance.
The variance is the average of the squared deviations. To find the variance, divide the sum of squared deviations by the number of values. In this case, the variance is 366 / 5 = 73.2.

Step 6: Find the standard deviation.
The standard deviation is the square root of the variance. In this case, the standard deviation is √73.2 ≈ 8.56 (rounded to two decimal places).

To summarize:
- The range is 25.
- The standard deviation is approximately 8.56.

By following these steps, you can calculate the range and standard deviation of any set of numbers.