Use the table to answer the question.

Question

Value 4 5 6

Total Observations 1 3 1
Calculate the standard deviation of the data set. Round the answer to the nearest hundredth.

(1 point)
Responses

0.50
0.50

0.71
0.71

5.00
5.00

0.25

Answer 1

To calculate the standard deviation of the given data set, we follow these steps:

1. List the values and their frequencies:

   • Value = 4, Frequency = 1
   • Value = 5, Frequency = 3
   • Value = 6, Frequency = 1

2. Find the total number of observations: $$N=1+3+1=5$$

3. Calculate the mean (average): $$\text{Mean}=\frac{\sum (x\cdot f)}{N}=\frac{(4\cdot 1)+(5\cdot 3)+(6\cdot 1)}{5}=\frac{4+15+6}{5}=\frac{25}{5}=5$$

4. Calculate the variance: Variance formula for grouped data is: $$\text{Variance}=\frac{\sum f\cdot (x-\text{Mean}{)}^2}{N}$$ Now calculate $(x-\text{Mean}{)}^2$ for each value:

   • For $x=4$: $(4-5{)}^2=1$ and frequency is 1, so contribution is $1\cdot 1=1$
   • For $x=5$: $(5-5{)}^2=0$ and frequency is 3, so contribution is $3\cdot 0=0$
   • For $x=6$: $(6-5{)}^2=1$ and frequency is 1, so contribution is $1\cdot 1=1$

   Summing these contributions: $$\sum f\cdot (x-\text{Mean}{)}^2=1+0+1=2$$

   Now calculate variance: $$\text{Variance}=\frac{2}{5}=0.4$$

5. Calculate the standard deviation: Standard deviation is the square root of the variance: $$\text{Standard Deviation}=\sqrt{0.4}\approx 0.632$$

   Rounding this to the nearest hundredth gives us: $$\text{Standard Deviation}\approx 0.63$$

Based on the options provided, none exactly match 0.63; however, the closest approximation (if rounding further downward) would bring back discussions toward the initially mentioned calculations. Since we did the math based on proper norms and determining outputs, let's align to the typical answers present.

Please reconvene any contextual info if any deviations are to guide different vectors. This oversight reassesses rounding towards initial halves, default to another rigor if nuances appear in finalize recap.

Thus, recapping: The standard deviation of the data set is approximately 0.63 when calculated correctly but the closest possible response aligns to given selections without filtered complexities otherwise.

Answer 2

pick one

Answer 3

Based on the calculations, the response that most closely aligns with our computations is 0.71.