| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | To compute the sample standard deviation of a set of numbers, we first need to calculate the mean of the numbers, then find the variance, and finally take the square root of the variance to get the standard deviation. Here are the steps: 1. Calculate the mean (average) of the numbers. 2. Subtract the mean from each number, square the result, and find the average (mean) of these squared differences. 3. Take the square root of the result from step 2 to get the sample standard deviation. Let's go through these steps with the given set of numbers: ${9, 14, 5, 4, -20, -13, -5, 13}$. Step 1: Calculate the mean. \[ \text{Mean} = \frac{9 + 14 + 5 + 4 + (-20) + (-13) + (-5) + 13}{8} = \frac{2}{8} = 0.25 \] Step 2: Subtract the mean from each number, square the result, and find the average of these squared differences. \[ (9 - 0.25)^2 = 72.25 \] \[ (14 - 0.25)^2 = 176.0625 \] \[ (5 - 0.25)^2 = 18.0625 \] \[ (4 - 0.25)^2 = 11.0625 \] \[ (-20 - 0.25)^2 = 407.5625 \] \[ (-13 - 0.25)^2 = 172.5625 \] \[ (-5 - 0.25)^2 = 26.0625 \] \[ (13 - 0.25)^2 = 151.5625 \] \[ \text{Average of squared differences} = \frac{72.25 + 176.0625 + 18.0625 + 11.0625 + 407.5625 + 172.5625 + 26.0625 + 151.5625}{8} = \frac{1035.25}{8} = 129.40625 \] Step 3: Take the square root of the result from step 2 to get the sample standard deviation. \[ \text{Sample Standard Deviation} = \sqrt{129.40625} = 11.376 \] Thus, the sample standard deviation of the given set of numbers is approximately $11.376$. **Final Answer:** $\boxed{11.376}$ |
\frac{\sqrt{\frac{8599}{14}}}{2} |
| deepseek-r1 | To compute the sample standard deviation of the dataset \({9, 14, 5, 4, -20, -13, -5, 13}\), follow these steps: 1. **Calculate the mean**: \[ \text{Mean} (\bar{x}) = \frac{9 + 14 + 5 + 4 + (-20) + (-13) + (-5) + 13}{8} = \frac{7}{8} = 0.875 \] 2. **Find the squared differences from the mean**: \[ \begin{aligned} (9 - 0.875)^2 &= 66.015625 \\ (14 - 0.875)^2 &= 172.265625 \\ (5 - 0.875)^2 &= 17.015625 \\ (4 - 0.875)^2 &= 9.765625 \\ (-20 - 0.875)^2 &= 435.765625 \\ (-13 - 0.875)^2 &= 192.515625 \\ (-5 - 0.875)^2 &= 34.515625 \\ (13 - 0.875)^2 &= 147.015625 \\ \end{aligned} \] 3. **Sum the squared differences**: \[ 66.015625 + 172.265625 + 17.015625 + 9.765625 + 435.765625 + 192.515625 + 34.515625 + 147.015625 = 1074.875 \] 4. **Calculate the sample variance**: \[ \text{Sample Variance} (s^2) = \frac{1074.875}{8 - 1} = \frac{1074.875}{7} \approx 153.553571429 \] 5. **Take the square root to find the sample standard deviation**: \[ \text{Sample Standard Deviation} (s) = \sqrt{153.553571429} \approx 12.3916 \] Rounding to two decimal places, the sample standard deviation is \(\boxed{12.39}\). |
\frac{\sqrt{\frac{8599}{14}}}{2} |
| gpto1 | To compute the sample standard deviation, we follow these steps: 1. **Calculate the mean (\( \mu \))**: \[ \mu = \frac{9 + 14 + 5 + 4 - 20 - 13 - 5 + 13}{8} = \frac{7}{8} = 0.875 \] 2. **Calculate the squared deviations and sum them**: \[ \begin{align*} & (9 - 0.875)^2 = 66.015625 \\ & (14 - 0.875)^2 = 172.265625 \\ & (5 - 0.875)^2 = 17.015625 \\ & (4 - 0.875)^2 = 9.765625 \\ & (-20 - 0.875)^2 = 435.765625 \\ & (-13 - 0.875)^2 = 192.515625 \\ & (-5 - 0.875)^2 = 34.515625 \\ & (13 - 0.875)^2 = 147.015625 \\ \text{Sum} &= 1074.875 \end{align*} \] 3. **Calculate the sample variance (\( s^2 \))**: \[ s^2 = \frac{1074.875}{8 - 1} = \frac{1074.875}{7} = 153.5535714 \] 4. **Calculate the sample standard deviation (\( s \))**: \[ s = \sqrt{153.5535714} \approx 12.392 \] **Final Answer:** \(\boxed{12.392}\) |
\frac{\sqrt{\frac{8599}{14}}}{2} |
| gpt-4o-2024-08-06 | To compute the sample standard deviation, we first need to find the mean of the data set, then calculate the variance, and finally take the square root of the variance. Given the data set: \( \{9, 14, 5, 4, -20, -13, -5, 13\} \). **Step 1: Calculate the mean.** The mean \(\bar{x}\) is given by: \[ \bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i \] where \( n \) is the number of data points. Here, \( n = 8 \). \[ \bar{x} = \frac{9 + 14 + 5 + 4 - 20 - 13 - 5 + 13}{8} \] Calculate the sum of the data points: \[ 9 + 14 + 5 + 4 - 20 - 13 - 5 + 13 = 7 \] Now, calculate the mean: \[ \bar{x} = \frac{7}{8} = 0.875 \] **Step 2: Calculate the variance.** The sample variance \( s^2 \) is given by: \[ s^2 = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2 \] Calculate each squared deviation from the mean: \[ (9 - 0.875)^2 = 66.015625 \] \[ (14 - 0.875)^2 = 173.140625 \] \[ (5 - 0.875)^2 = 17.015625 \] \[ (4 - 0.875)^2 = 9.765625 \] \[ (-20 - 0.875)^2 = 428.265625 \] \[ (-13 - 0.875)^2 = 194.765625 \] \[ (-5 - 0.875)^2 = 34.765625 \] \[ (13 - 0.875)^2 = 147.015625 \] Sum of squared deviations: \[ 66.015625 + 173.140625 + 17.015625 + 9.765625 + 428.265625 + 194.765625 + 34.765625 + 147.015625 = 1070.75 \] Now, calculate the variance: \[ s^2 = \frac{1070.75}{8-1} = \frac{1070.75}{7} = 152.9642857 \] **Step 3: Calculate the standard deviation.** The sample standard deviation \( s \) is the square root of the variance: \[ s = \sqrt{152.9642857} \approx 12.369 \] Thus, the sample standard deviation is: \[ \boxed{12.369} \] |
\frac{\sqrt{\frac{8599}{14}}}{2} |
| DeepSeek-Coder-V2-Lite-Instruct | To compute the sample standard deviation, we follow these steps: 1. **Calculate the mean (average) of the data set.** 2. **Find the variance.** 3. **Take the square root of the variance to get the standard deviation.** Let's go through these steps one by one. ### Step 1: Calculate the mean The data set is: \( \{9, 14, 5, 4, -20, -13, -5, 13\} \) First, sum all the numbers: \[ 9 + 14 + 5 + 4 - 20 - 13 - 5 + 13 \] Let's add them step by step: \[ 9 + 14 = 23 \] \[ 23 + 5 = 28 \] \[ 28 + 4 = 32 \] \[ 32 - 20 = 12 \] \[ 12 - 13 = -1 \] \[ -1 - 5 = -6 \] \[ -6 + 13 = 7 \] So, the sum of the data set is \( 7 \). Next, divide the sum by the number of data points to find the mean: \[ \text{Mean} = \frac{7}{8} = 0.875 \] ### Step 2: Find the variance The variance is calculated by finding the average of the squared differences from the mean. First, calculate the squared differences from the mean: \[ (9 - 0.875)^2 = 8.125^2 = 66.015625 \] \[ (14 - 0.875)^2 = 13.125^2 = 172.265625 \] \[ (5 - 0.875)^2 = 4.125^2 = 17.015625 \] \[ (4 - 0.875)^2 = 3.125^2 = 9.765625 \] \[ (-20 - 0.875)^2 = -20.875^2 = 435.765625 \] \[ (-13 - 0.875)^2 = -13.875^2 = 192.515625 \] \[ (-5 - 0.875)^2 = -5.875^2 = 34.515625 \] \[ (13 - 0.875)^2 = 12.125^2 = 147.015625 \] Next, sum these squared differences: \[ 66.015625 + 172.265625 + 17.015625 + 9.765625 + 435.765625 + 192.515625 + 34.515625 + 147.015625 \] Let's add them step by step: \[ 66.015625 + 172.265625 = 238.28125 \] \[ 238.28125 + 17.015625 = 255.296875 \] \[ 255.296875 + 9.765625 = 265.0625 \] \[ 265.0625 + 435.765625 = 700.828125 \] \[ 700.828125 + 192.515625 = 893.34375 \] \[ 893.34375 + 34.515625 = 927.859375 \] \[ 927.859375 + 147.015625 = 1074.875 \] So, the sum of the squared differences is \( 1074.875 \). Now, divide this sum by the number of data points minus one (since we are calculating the sample standard deviation): \[ \text{Variance} = \frac{1074.875}{8 - 1} = \frac{1074.875}{7} = 153.5535714 \] ### Step 3: Calculate the sample standard deviation The sample standard deviation is the square root of the variance: \[ \text{Standard Deviation} = \sqrt{153.5535714} \approx 12.39 \] However, the final answer should be in the format \(\boxed{}\) with the exact value. Therefore, the final answer is: \[ \boxed{12.39} \] |
\frac{\sqrt{\frac{8599}{14}}}{2} |
| Meta-Llama-3.1-405B-Instruct-Turbo | ## Step 1: Calculate the mean of the given data set. To find the mean, we sum up all the numbers and then divide by the total count of numbers. The data set is ${9, 14, 5, 4, -20, -13, -5, 13}$. The sum is $9 + 14 + 5 + 4 - 20 - 13 - 5 + 13 = 7$. There are 8 numbers in the data set, so the mean is $7 / 8 = 0.875$. ## Step 2: Calculate the variance of the data set. To find the variance, we first need to find the deviation of each number from the mean, then square each deviation, sum these squared deviations, and finally divide by the number of items minus one (for sample variance). The deviations from the mean are $(9-0.875), (14-0.875), (5-0.875), (4-0.875), (-20-0.875), (-13-0.875), (-5-0.875), (13-0.875)$, which simplifies to $8.125, 13.125, 4.125, 3.125, -20.875, -13.875, -5.875, 12.125$. Squaring these gives $66.015625, 172.265625, 17.015625, 9.765625, 435.765625, 192.515625, 34.515625, 147.015625$. Summing these squares gives $1075.078125$. Dividing by 7 (the number of items minus one) gives a variance of $153.582591$ (rounded to six decimal places for the sake of precision in the next steps). ## Step 3: Calculate the sample standard deviation. The sample standard deviation is the square root of the variance. So, we take the square root of $153.582591$. The final answer is: $\boxed{12.38}$ |
\frac{\sqrt{\frac{8599}{14}}}{2} |
| Meta-Llama-3.1-70B-Instruct-Turbo | ## Step 1: Calculate the mean of the given data set To find the sample standard deviation, we first need to calculate the mean of the given data set. The mean is calculated by summing up all the numbers and then dividing by the total count of numbers. The given data set is ${9, 14, 5, 4, -20, -13, -5, 13}$. The sum of these numbers is $9 + 14 + 5 + 4 - 20 - 13 - 5 + 13 = 7$. There are 8 numbers in the data set. Therefore, the mean is $7 / 8 = 0.875$. ## Step 2: Subtract the mean from each data point to find the deviations Next, we subtract the mean from each data point to find the deviations from the mean. The deviations are $(9 - 0.875), (14 - 0.875), (5 - 0.875), (4 - 0.875), (-20 - 0.875), (-13 - 0.875), (-5 - 0.875), (13 - 0.875)$. This simplifies to $8.125, 13.125, 4.125, 3.125, -20.875, -13.875, -4.875, 12.125$. ## Step 3: Square each deviation Now, we square each deviation. The squared deviations are $8.125^2, 13.125^2, 4.125^2, 3.125^2, -20.875^2, -13.875^2, -4.875^2, 12.125^2$. This simplifies to $66.015625, 172.265625, 17.015625, 9.765625, 435.515625, 192.765625, 23.765625, 147.015625$. ## Step 4: Calculate the sum of the squared deviations We then calculate the sum of the squared deviations. The sum is $66.015625 + 172.265625 + 17.015625 + 9.765625 + 435.515625 + 192.765625 + 23.765625 + 147.015625 = 1063.33375$. ## Step 5: Divide the sum of the squared deviations by the number of data points minus one To calculate the sample variance, we divide the sum of the squared deviations by the number of data points minus one. In this case, we divide by $8 - 1 = 7$. Therefore, the sample variance is $1063.33375 / 7 = 151.9048225$. ## Step 6: Take the square root of the sample variance to find the sample standard deviation Finally, we take the square root of the sample variance to find the sample standard deviation. The square root of $151.9048225$ is approximately $12.32$. The final answer is: $\boxed{12.32}$ |
\frac{\sqrt{\frac{8599}{14}}}{2} |
| Qwen2-72B-Instruct | To compute the sample standard deviation of a set of numbers, we follow these steps: 1. Calculate the mean (average) of the numbers. 2. Subtract the mean from each number to find its deviation from the mean. 3. Square each deviation. 4. Find the average of these squared deviations (this is called the variance). 5. Take the square root of the variance to get the standard deviation. Let's calculate it step by step for the given set of numbers: ${9, 14, 5, 4, -20, -13, -5, 13}$. Step 1: Calculate the mean \[ \text{Mean} = \frac{\sum x_i}{n} = \frac{9 + 14 + 5 + 4 + (-20) + (-13) + (-5) + 13}{8} \] \[ = \frac{2}{8} = 0.25 \] Step 2: Subtract the mean from each number \[ x_i - \text{mean} = \{8.75, 13.75, 4.75, 3.75, -20.25, -13.25, -5.25, 12.75\} \] Step 3: Square each deviation \[ (x_i - \text{mean})^2 = \{76.5625, 189.0625, 22.5625, 14.0625, 410.0625, 175.5625, 27.5625, 162.5625\} \] Step 4: Find the average of these squared deviations (variance) \[ \text{Variance} = \frac{\sum (x_i - \text{mean})^2}{n-1} = \frac{76.5625 + 189.0625 + 22.5625 + 14.0625 + 410.0625 + 175.5625 + 27.5625 + 162.5625}{7} \] \[ = \frac{1077.9375}{7} = 153.99107142857143 \] Step 5: Take the square root of the variance to get the standard deviation \[ \text{Standard Deviation} = \sqrt{153.99107142857143} \approx 12.4093 \] Therefore, the sample standard deviation of the given set of numbers is approximately $\boxed{12.41}$. |
\frac{\sqrt{\frac{8599}{14}}}{2} |
| baichuan4 | To compute the sample standard deviation of a set of numbers, we first need to calculate the mean (average) of the numbers. Then, for each number, we find the difference between that number and the mean. We square each of these differences, sum them up, and then divide by the number of elements in the set minus one (since we are dealing with the sample standard deviation). Finally, we take the square root of this result to obtain the sample standard deviation. Given the set of numbers: $$9, 14, 5, 4, -20, -13, -5, 13$$ First, we calculate the mean: $$\text{Mean} = \frac{9 + 14 + 5 + 4 - 20 - 13 - 5 + 13}{8} = \frac{0}{8} = 0$$ Next, we find the differences between each number and the mean, square them, and sum them up: $$\sum (x_i - \text{Mean})^2 = (9 - 0)^2 + (14 - 0)^2 + (5 - 0)^2 + (4 - 0)^2 + (-20 - 0)^2 + (-13 - 0)^2 + (-5 - 0)^2 + (13 - 0)^2$$ $$= 81 + 196 + 25 + 16 + 400 + 169 + 25 + 169$$ $$= 1081$$ Now, we divide this sum by the number of elements in the set minus one: $$\text{Sample Variance} = \frac{1081}{8 - 1} = \frac{1081}{7} \approx 154.43$$ Finally, we take the square root of the sample variance to obtain the sample standard deviation: $$\text{Sample Standard Deviation} = \sqrt{154.43} \approx 12.43$$ Therefore, the sample standard deviation of the given set of numbers is approximately $12.43$. $$\boxed{12.43}$$ |
\frac{\sqrt{\frac{8599}{14}}}{2} |
| doubao | First find the mean: $(9+14+5+4-20-13-5+13)\div8$ $=(23+5+4-20-13-5+13)\div8$ $=(28+4-20-13-5+13)\div8$ $=(32-20-13-5+13)\div8$ $=(12-13-5+13)\div8$ $=(-1-5+13)\div8$ $=(-6+13)\div8$ $=7\div8=\frac{7}{8}$ Then calculate the deviations from the mean for each value: $(9-\frac{7}{8})^2=(\frac{72}{8}-\frac{7}{8})^2=(\frac{65}{8})^2=\frac{4225}{64}$ $(14-\frac{7}{8})^2=(\frac{112}{8}-\frac{7}{8})^2=(\frac{105}{8})^2=\frac{11025}{64}$ $(5-\frac{7}{8})^2=(\frac{40}{8}-\frac{7}{8})^2=(\frac{33}{8})^2=\frac{1089}{64}$ $(4-\frac{7}{8})^2=(\frac{32}{8}-\frac{7}{8})^2=(\frac{25}{8})^2=\frac{625}{64}$ $(-20-\frac{7}{8})^2=(-\frac{160}{8}-\frac{7}{8})^2=(-\frac{167}{8})^2=\frac{27889}{64}$ $(-13-\frac{7}{8})^2=(-\frac{104}{8}-\frac{7}{8})^2=(-\frac{111}{8})^2=\frac{12321}{64}$ $(-5-\frac{7}{8})^2=(-\frac{40}{8}-\frac{7}{8})^2=(-\frac{47}{8})^2=\frac{2209}{64}$ $(13-\frac{7}{8})^2=(\frac{104}{8}-\frac{7}{8})^2=(\frac{97}{8})^2=\frac{9409}{64}$ The sum of the squared deviations is: $\frac{4225}{64}+\frac{11025}{64}+\frac{1089}{64}+\frac{625}{64}+\frac{27889}{64}+\frac{12321}{64}+\frac{2209}{64}+\frac{9409}{64}$ $=\frac{4225+11025+1089+625+27889+12321+2209+9409}{64}$ $=\frac{68793}{64}$ The sample variance is the sum of the squared deviations divided by $n-1$ (where $n$ is the number of values), so the variance is: $\frac{68793}{64}\div(8-1)=\frac{68793}{64}\div7=\frac{68793}{448}$ The sample standard deviation is the square root of the variance, so: $\sqrt{\frac{68793}{448}}=\boxed{\frac{\sqrt{275172}}{56}}$. |
\frac{\sqrt{\frac{8599}{14}}}{2} |
| gpto1 | To compute the sample standard deviation, we follow these steps: 1. **Calculate the mean (\( \mu \))**: \[ \mu = \frac{9 + 14 + 5 + 4 - 20 - 13 - 5 + 13}{8} = \frac{7}{8} = 0.875 \] 2. **Calculate the squared deviations and sum them**: \[ \begin{align*} & (9 - 0.875)^2 = 66.015625 \\ & (14 - 0.875)^2 = 172.265625 \\ & (5 - 0.875)^2 = 17.015625 \\ & (4 - 0.875)^2 = 9.765625 \\ & (-20 - 0.875)^2 = 435.765625 \\ & (-13 - 0.875)^2 = 192.515625 \\ & (-5 - 0.875)^2 = 34.515625 \\ & (13 - 0.875)^2 = 147.015625 \\ \text{Sum} &= 1074.875 \end{align*} \] 3. **Calculate the sample variance (\( s^2 \))**: \[ s^2 = \frac{1074.875}{8 - 1} = \frac{1074.875}{7} = 153.5535714 \] 4. **Calculate the sample standard deviation (\( s \))**: \[ s = \sqrt{153.5535714} \approx 12.392 \] **Final Answer:** \(\boxed{12.392}\) |
\frac{\sqrt{\frac{8599}{14}}}{2} |
| kimi | First, calculate the mean of the numbers: \[ \text{Mean} = \frac{9 + 14 + 5 + 4 - 20 - 13 - 5 + 13}{8} = \frac{1}{8} = 0.125 \] Next, calculate the squared differences from the mean, and then find their average: \[ \frac{(9-0.125)^2 + (14-0.125)^2 + (5-0.125)^2 + (4-0.125)^2 + (-20-0.125)^2 + (-13-0.125)^2 + (-5-0.125)^2 + (13-0.125)^2}{8} \] \[ = \frac{(8.875)^2 + (13.875)^2 + (4.875)^2 + (3.875)^2 + (-20.125)^2 + (-13.125)^2 + (-5.125)^2 + (12.875)^2}{8} \] \[ = \frac{78.765625 + 192.515625 + 23.890625 + 15.015625 + 404.765625 + 171.765625 + 26.390625 + 166.515625}{8} \] \[ = \frac{1247.875}{8} = 155.984375 \] The variance is thus $155.984375$. The sample standard deviation is the square root of the variance: \[ \sqrt{155.984375} \approx 12.492765 \] Thus, the sample standard deviation is $\boxed{12.5}$ (rounded to the nearest tenth). |
\frac{\sqrt{\frac{8599}{14}}}{2} |
| minimax | To compute the sample standard deviation of the given data set ${9, 14, 5, 4, -20, -13, -5, 13}$, we will follow these steps: 1. Find the mean (average) of the data set. 2. Subtract the mean from each data point and square the result (the squared difference). 3. Find the mean of those squared differences. 4. Take the square root of the mean of the squared differences to get the standard deviation. Let's go through these steps: 1. Calculate the mean: $$ \text{Mean} = \frac{9 + 14 + 5 + 4 + (-20) + (-13) + (-5) + 13}{8} $$ $$ \text{Mean} = \frac{9 + 14 + 5 + 4 - 20 - 13 - 5 + 13}{8} $$ $$ \text{Mean} = \frac{7}{8} $$ $$ \text{Mean} = 0.875 $$ 2. Calculate the squared differences from the mean: $$ (9 - 0.875)^ |
\frac{\sqrt{\frac{8599}{14}}}{2} |
| wenxinyiyan | 计算过程如下： 首先，我们需要计算这组数据的平均值。 平均值 $\bar{x}$ 的计算公式是： $$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$ 其中 $n$ 是数据点的个数，$x_i$ 是每个数据点。 给定的数据是 ${9, 14, 5, 4, -20, -13, -5, 13}$，数据点的个数 $n = 8$。 计算平均值： $$\bar{x} = \frac{9 + 14 + 5 + 4 - 20 - 13 - 5 + 13}{8} = \frac{7}{8} = 0.875$$ 接下来，我们计算每个数据点与平均值的差的平方，然后求这些平方差的平均值。 方差 $s^2$ 的计算公式是： $$s^2 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n-1}$$ 计算方差： $$s^2 = \frac{(9-0.875)^2 + (14-0.875)^2 + (5-0.875)^2 + (4-0.875)^2 + (-20-0.875)^2 + (-13-0.875)^2 + (-5-0.875)^2 + (13-0.875)^2}{8-1}$$ $$s^2 = \frac{(8.125)^2 + (13.125)^2 + (4.125)^2 + (3.125)^2 + (-20.875)^2 + (-13.875)^2 + (-5.875)^2 + (12.125)^2}{7}$$ $$s^2 = \frac{66.015625 + 172.390625 + 17.015625 + 9.765625 + 435.765625 + 192.515625 + 34.515625 + 147.015625}{7}$$ $$s^2 = \frac{1075.0078125}{7} \approx 153.5725$$ 最后，我们计算方差的平方根，得到样本标准偏差。 样本标准偏差 $s$ 的计算公式是： $$s = \sqrt{s^2}$$ 计算样本标准偏差： $$s = \sqrt{153.5725} \approx 12.4$$ 所以，样本标准偏差是 $\boxed{12.4}$。 |
\frac{\sqrt{\frac{8599}{14}}}{2} |
| zhipu | 1. **Calculate the mean of the data set**: \[ \text{Mean} = \frac{9 + 14 + 5 + 4 - 20 - 13 - 5 + 13}{8} = \frac{-1}{8} = -0.125 \] 2. **Calculate the squared deviations from the mean for each data point**: - $(9 + 0.125)^2 = (9.125)^2 = 83.515625$ - $(14 + 0.125)^2 = (14.125)^2 = 200.390625$ - $(5 + 0.125)^2 = (5.125)^2 = 26.265625$ - $(4 + 0.125)^2 = (4.125)^2 = 17.015625$ - $(-20 + 0.125)^2 = (-19.875)^2 = 395.015625$ - $(-13 + 0.125)^2 = (-12.875)^2 = 165.890625$ - $(-5 + 0.125)^2 = (-4.875)^2 = 23.765625$ - $(13 + 0.125)^2 = (13.125)^2 = 172.265625$ 3. **Sum the squared deviations**: \[ \text{Sum of squared deviations} = 83.515625 + 200.390625 + 26.265625 + 17.015625 + 395.015625 + 165.890625 + 23.765625 + 172.265625 = 1094.81375 \] 4. **Calculate the variance**: \[ \text{Variance} = \frac{\text{Sum of squared deviations}}{n - 1} = \frac{1094.81375}{7} \approx 156.4020535714 \] 5. **Calculate the standard deviation**: \[ \text{Standard Deviation} = \sqrt{\text{Variance}} = \sqrt{156.4020535714} \approx 12.502 \] Thus, the sample standard deviation of the data set is $\\boxed{12.502}$. |
\frac{\sqrt{\frac{8599}{14}}}{2} |
| deepseek-v3 | Error code: 400 - {'error': {'code': 'RequestTimeOut', 'param': None, 'message': 'Request timed out, please try again later.', 'type': 'RequestTimeOut'}, 'id': 'chatcmpl-c14c8227-4f7a-9b5d-8f07-3706ce472ed5', 'request_id': 'c14c8227-4f7a-9b5d-8f07-3706ce472ed5'} | \frac{\sqrt{\frac{8599}{14}}}{2} |