A sample of size $$ n=10 $$ is drawn from a population. The data is shown below. $$ \begin{array}{ccccc} 115 & 98.8 & 115 & 105.3 & 99 \ 115 & 87.9 & 92.2 & 85.9 & 76.1 \end{array} $$ What is the range of this data set? range = $$ \square $$ What is the standard deviation of this data set? (Round to 2 decimal places) stdev $$ = $$ $$ \square $$ 734

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**Step 1. Calculate the range**

The range is given by  
$$
\text{range} = \text{maximum value} - \text{minimum value}.
$$

From the data, the maximum is $$115$$ and the minimum is $$76.1$$. Thus,
$$
\text{range} = 115 - 76.1 = 38.9.
$$

**Step 2. Calculate the sample standard deviation**

First, find the mean $$\bar{x}$$:
$$
\bar{x} = \frac{115 + 98.8 + 115 + 105.3 + 99 + 115 + 87.9 + 92.2 + 85.9 + 76.1}{10}.
$$

Adding the values:
$$
115 + 98.8 + 115 + 105.3 + 99 + 115 + 87.9 + 92.2 + 85.9 + 76.1 = 990.2.
$$

Thus,
$$
\bar{x} = \frac{990.2}{10} = 99.02.
$$

Next, calculate each squared deviation $$(x_i - \bar{x})^2$$:

1. For $$115$$: 
   $$
   (115 - 99.02)^2 = (15.98)^2 \approx 255.36.
   $$
2. For $$98.8$$: 
   $$
   (98.8 - 99.02)^2 = (-0.22)^2 \approx 0.0484.
   $$
3. For $$115$$ (again): 
   $$
   (15.98)^2 \approx 255.36.
   $$
4. For $$105.3$$: 
   $$
   (105.3 - 99.02)^2 = (6.28)^2 \approx 39.44.
   $$
5. For $$99$$: 
   $$
   (99 - 99.02)^2 = (-0.02)^2 \approx 0.0004.
   $$
6. For $$115$$ (another one): 
   $$
   (15.98)^2 \approx 255.36.
   $$
7. For $$87.9$$: 
   $$
   (87.9 - 99.02)^2 = (-11.12)^2 \approx 123.65.
   $$
8. For $$92.2$$: 
   $$
   (92.2 - 99.02)^2 = (-6.82)^2 \approx 46.51.
   $$
9. For $$85.9$$: 
   $$
   (85.9 - 99.02)^2 = (-13.12)^2 \approx 172.13.
   $$
10. For $$76.1$$: 
    $$
    (76.1 - 99.02)^2 = (-22.92)^2 \approx 525.09.
    $$

Now, sum the squared deviations:
$$
255.36 + 0.0484 + 255.36 + 39.44 + 0.0004 + 255.36 + 123.65 + 46.51 + 172.13 + 525.09 \approx 1672.95.
$$

The sample variance is:
$$
s^2 = \frac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n-1} = \frac{1672.95}{10-1} = \frac{1672.95}{9} \approx 185.88.
$$

Taking the square root gives the sample standard deviation:
$$
s = \sqrt{185.88} \approx 13.64.
$$

**Final Answers:**

- Range $$ = 38.9 $$
- Standard Deviation $$ \approx 13.64 $$
Range = 38.9 Standard Deviation ≈ 13.64

A sample of size is drawn from a population. The data is shown below.

What is the range of this data set?
range =

What is the standard deviation of this data set? (Round to 2 decimal places)
stdev 734

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A sample of size is drawn from a population. The data is shown below. What is the range of this data set? range = What is the standard deviation of this data set? (Round to 2 decimal places) stdev 734