To find the range and standard deviation of the given data set, let's follow these steps:

Step 1: Calculate the Range

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

1. Identify the maximum and minimum values:

   • Maximum value: 95
   • Minimum value: 12

2. Calculate the range: $\text{Range} = \text{Maximum} - \text{Minimum} = 95 - 12 = 83$

Step 2: Calculate the Standard Deviation

The standard deviation measures the amount of variation or dispersion in a set of values.

1. Calculate the mean (average) of the data set.

$\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$

2. Find the squared differences from the mean for each data point.

3. Calculate the variance, which is the average of the squared differences.

4. Take the square root of the variance to get the standard deviation.

Let's compute these using the given data.

Data Set

$27, 74, 89, 36, 50, 81, 27, 90, 83, 44, 57, 68, 60, 24, 33, 58, 74, 47, 24, 30, 27, 90, 95, 12$

Now let's calculate it step-by-step using Python.The results for the given data set are:

• Range = 83
• Standard Deviation = 25.32

Would you like more details on the calculations or have any questions?

Related Questions:

1. How is the variance different from the standard deviation?
2. What is the difference between population and sample standard deviation?
3. How can outliers affect the standard deviation?
4. How do you interpret the standard deviation in the context of a data set?
5. What is the importance of calculating the range in a data set?

Tip:

To better understand data dispersion, always consider both the range and standard deviation together, as they provide different insights into data variability.