| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | To compute the sample variance of the set \(\{-22, 22, 11, -19, 8, 7\}\), we follow these steps: 1. **Calculate the mean (average) of the data set:** \[ \text{Mean} = \frac{-22 + 22 + 11 + -19 + 8 + 7}{6} \] \[ \text{Mean} = \frac{-22 + 22 + 11 - 19 + 8 + 7}{6} \] \[ \text{Mean} = \frac{-22 + 22 + 11 - 19 + 8 + 7}{6} = \frac{-3}{6} = -0.5 \] 2. **Calculate the squared differences from the mean for each data point:** \[ (-22 - (-0.5))^2 = (-22 + 0.5)^2 = (-21.5)^2 = 462.25 \] \[ (22 - (-0.5))^2 = (22 + 0.5)^2 = (22.5)^2 = 506.25 \] \[ (11 - (-0.5))^2 = (11 + 0.5)^2 = (11.5)^2 = 132.25 \] \[ (-19 - (-0.5))^2 = (-19 + 0.5)^2 = (-18.5)^2 = 342.25 \] \[ (8 - (-0.5))^2 = (8 + 0.5)^2 = (8.5)^2 = 72.25 \] \[ (7 - (-0.5))^2 = (7 + 0.5)^2 = (7.5)^2 = 56.25 \] 3. **Sum the squared differences:** \[ 462.25 + 506.25 + 132.25 + 342.25 + 72.25 + 56.25 = 1571.5 \] 4. **Divide the sum of squared differences by \(n-1\) (where \(n\) is the number of data points):** \[ \text{Sample Variance} = \frac{1571.5}{6-1} = \frac{1571.5}{5} = 314.3 \] Thus, the sample variance is: \[ \boxed{314.3} \] |
\frac{9329}{30} |
| deepseek-r1 | To compute the sample variance of the data set \(\{-22, 22, 11, -19, 8, 7\}\), we follow these steps: 1. **Calculate the mean**: \[ \bar{x} = \frac{-22 + 22 + 11 - 19 + 8 + 7}{6} = \frac{7}{6} \] 2. **Compute the squared differences from the mean** for each data point: \[ \begin{aligned} (-22 - \frac{7}{6})^2 &= \left(-\frac{139}{6}\right)^2 = \frac{19321}{36}, \\ (22 - \frac{7}{6})^2 &= \left(\frac{125}{6}\right)^2 = \frac{15625}{36}, \\ (11 - \frac{7}{6})^2 &= \left(\frac{59}{6}\right)^2 = \frac{3481}{36}, \\ (-19 - \frac{7}{6})^2 &= \left(-\frac{121}{6}\right)^2 = \frac{14641}{36}, \\ (8 - \frac{7}{6})^2 &= \left(\frac{41}{6}\right)^2 = \frac{1681}{36}, \\ (7 - \frac{7}{6})^2 &= \left(\frac{35}{6}\right)^2 = \frac{1225}{36}. \end{aligned} \] 3. **Sum the squared differences**: \[ \frac{19321}{36} + \frac{15625}{36} + \frac{3481}{36} + \frac{14641}{36} + \frac{1681}{36} + \frac{1225}{36} = \frac{55974}{36} \] 4. **Divide by \(n - 1\)** (where \(n = 6\)): \[ s^2 = \frac{\frac{55974}{36}}{5} = \frac{55974}{180} = \frac{9329}{30} \] Thus, the sample variance is \(\boxed{\dfrac{9329}{30}}\). |
\frac{9329}{30} |
| gpto1 | To compute the sample variance of the set \(-22, 22, 11, -19, 8, 7\), we'll follow these steps: **Step 1: Compute the sample mean (\(\mu\))** \[ \mu = \frac{\sum x_i}{n} = \frac{-22 + 22 + 11 - 19 + 8 + 7}{6} = \frac{7}{6} = \frac{7}{6} \] **Step 2: Compute each deviation from the mean and square it.** Let's find \(x_i - \mu\) and \((x_i - \mu)^2\) for each data point: 1. \(x_1 = -22\) \[ x_1 - \mu = -22 - \frac{7}{6} = -\frac{139}{6} \] \[ (x_1 - \mu)^2 = \left(-\frac{139}{6}\right)^2 = \frac{19321}{36} \] 2. \(x_2 = 22\) \[ x_2 - \mu = 22 - \frac{7}{6} = \frac{125}{6} \] \[ (x_2 - \mu)^2 = \left(\frac{125}{6}\right)^2 = \frac{15625}{36} \] 3. \(x_3 = 11\) \[ x_3 - \mu = 11 - \frac{7}{6} = \frac{59}{6} \] \[ (x_3 - \mu)^2 = \left(\frac{59}{6}\right)^2 = \frac{3481}{36} \] 4. \(x_4 = -19\) \[ x_4 - \mu = -19 - \frac{7}{6} = -\frac{121}{6} \] \[ (x_4 - \mu)^2 = \left(-\frac{121}{6}\right)^2 = \frac{14641}{36} \] 5. \(x_5 = 8\) \[ x_5 - \mu = 8 - \frac{7}{6} = \frac{41}{6} \] \[ (x_5 - \mu)^2 = \left(\frac{41}{6}\right)^2 = \frac{1681}{36} \] 6. \(x_6 = 7\) \[ x_6 - \mu = 7 - \frac{7}{6} = \frac{35}{6} \] \[ (x_6 - \mu)^2 = \left(\frac{35}{6}\right)^2 = \frac{1225}{36} \] **Step 3: Sum the squared deviations and compute the variance** \[ \text{Sum of squared deviations} = \frac{19321 + 15625 + 3481 + 14641 + 1681 + 1225}{36} = \frac{55974}{36} \] Since we're calculating the **sample variance**, we divide by \(n - 1\) (degrees of freedom), where \(n = 6\): \[ s^2 = \frac{\text{Sum of squared deviations}}{n - 1} = \frac{\frac{55974}{36}}{5} = \frac{55974}{180} = \frac{9331}{30} \] **Answer:** \[\boxed{\dfrac{9331}{30}}\] |
\frac{9329}{30} |
| gpt-4o-2024-08-06 | To compute the sample variance, we first need to find the sample mean and then use it to calculate the variance. Given the data set: \(-22, 22, 11, -19, 8, 7\). **Step 1: Calculate the sample mean.** The formula for the sample mean \(\bar{x}\) is: \[ \bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i \] where \(n\) is the number of data points. Here, \(n = 6\). \[ \bar{x} = \frac{-22 + 22 + 11 - 19 + 8 + 7}{6} \] Calculate the sum of the data points: \[ -22 + 22 + 11 - 19 + 8 + 7 = 7 \] Now, calculate the mean: \[ \bar{x} = \frac{7}{6} \approx 1.1667 \] **Step 2: Calculate the sample variance.** The formula for the sample variance \(s^2\) is: \[ s^2 = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2 \] Substitute \(n = 6\) and \(\bar{x} \approx 1.1667\): \[ s^2 = \frac{1}{5} \left[(-22 - 1.1667)^2 + (22 - 1.1667)^2 + (11 - 1.1667)^2 + (-19 - 1.1667)^2 + (8 - 1.1667)^2 + (7 - 1.1667)^2\right] \] Calculate each squared deviation: 1. \((-22 - 1.1667)^2 = (-23.1667)^2 \approx 536.0278\) 2. \((22 - 1.1667)^2 = (20.8333)^2 \approx 434.0278\) 3. \((11 - 1.1667)^2 = (9.8333)^2 \approx 96.6944\) 4. \((-19 - 1.1667)^2 = (-20.1667)^2 \approx 406.6944\) 5. \((8 - 1.1667)^2 = (6.8333)^2 \approx 46.6944\) 6. \((7 - 1.1667)^2 = (5.8333)^2 \approx 34.0278\) Sum of squared deviations: \[ 536.0278 + 434.0278 + 96.6944 + 406.6944 + 46.6944 + 34.0278 = 1554.1666 \] Now, calculate the sample variance: \[ s^2 = \frac{1554.1666}{5} = 310.8333 \] Thus, the sample variance is: \[ \boxed{310.8333} \] |
\frac{9329}{30} |
| DeepSeek-Coder-V2-Lite-Instruct | To compute the sample variance of the list \({-22, 22, 11, -19, 8, 7}\), we follow these steps: 1. **Calculate the mean (average) of the numbers:** \[ \text{Mean} = \frac{-22 + 22 + 11 - 19 + 8 + 7}{6} \] \[ \text{Mean} = \frac{5}{6} \] 2. **Calculate the squared differences from the mean:** \[ (-22 - \frac{5}{6})^2 = \left(-\frac{137}{6}\right)^2 = \frac{18769}{36} \] \[ (22 - \frac{5}{6})^2 = \left(\frac{127}{6}\right)^2 = \frac{16129}{36} \] \[ (11 - \frac{5}{6})^2 = \left(\frac{61}{6}\right)^2 = \frac{3721}{36} \] \[ (-19 - \frac{5}{6})^2 = \left(-\frac{119}{6}\right)^2 = \frac{14161}{36} \] \[ (8 - \frac{5}{6})^2 = \left(\frac{43}{6}\right)^2 = \frac{1849}{36} \] \[ (7 - \frac{5}{6})^2 = \left(\frac{37}{6}\right)^2 = \frac{1369}{36} \] 3. **Sum the squared differences:** \[ \sum \left( x_i - \bar{x} \right)^2 = \frac{18769}{36} + \frac{16129}{36} + \frac{3721}{36} + \frac{14161}{36} + \frac{1849}{36} + \frac{1369}{36} \] \[ \sum \left( x_i - \bar{x} \right)^2 = \frac{18769 + 16129 + 3721 + 14161 + 1849 + 1369}{36} \] \[ \sum \left( x_i - \bar{x} \right)^2 = \frac{56008}{36} \] 4. **Divide by the number of elements minus one (n-1):** \[ \text{Sample Variance} = \frac{\sum \left( x_i - \bar{x} \right)^2}{n-1} = \frac{\frac{56008}{36}}{6-1} = \frac{\frac{56008}{36}}{5} = \frac{56008}{180} = \frac{7001}{22.5} = 311.15555555555554 \] 5. **Round to a reasonable number of decimal places (if necessary):** \[ \text{Sample Variance} \approx 311.16 \] However, the final answer should be in the form of $\boxed{}$. Therefore, the final answer is: \[ \boxed{311.16} \] |
\frac{9329}{30} |
| Meta-Llama-3.1-405B-Instruct-Turbo | ## Step 1: Calculate the sample mean To find the sample variance, we first need to calculate the sample mean. The sample mean is the average of all the numbers in the dataset. The dataset is ${-22, 22, 11, -19, 8, 7}$. We add up all the numbers and divide by the total count of numbers. ## Step 2: Sum up all the numbers in the dataset $-22 + 22 + 11 - 19 + 8 + 7 = 7$ ## Step 3: Calculate the sample mean The total count of numbers is 6. So, the sample mean is $7 / 6 = 1.1667$. ## Step 4: Calculate the deviations from the mean Next, we need to find the deviations of each number from the sample mean. ## Step 5: Calculate the squared deviations The squared deviations are $(-22-1.1667)^2, (22-1.1667)^2, (11-1.1667)^2, (-19-1.1667)^2, (8-1.1667)^2, (7-1.1667)^2$. ## Step 6: Calculate the squared deviations $(-23.1667)^2 = 536.1111, (20.8333)^2 = 433.8889, (9.8333)^2 = 96.6667, (-20.1667)^2 = 406.8889, (6.8333)^2 = 46.6667, (5.8333)^2 = 34.1667$. ## Step 7: Calculate the sum of the squared deviations $536.1111 + 433.8889 + 96.6667 + 406.8889 + 46.6667 + 34.1667 = 1554.3889$. ## Step 8: Calculate the sample variance The sample variance is the sum of the squared deviations divided by the total count of numbers minus 1. So, the sample variance is $1554.3889 / (6 - 1) = 310.8778$. The final answer is: $\boxed{310.8778}$ |
\frac{9329}{30} |
| Meta-Llama-3.1-70B-Instruct-Turbo | ## Step 1: Calculate the sample mean To find the sample variance, we first need to calculate the sample mean. The sample mean is calculated by summing all the values and dividing by the number of values. The values given are ${-22, 22, 11, -19, 8, 7}$. The sum of these values is $-22 + 22 + 11 - 19 + 8 + 7 = 7$. There are 6 values in total. Therefore, the sample mean is $7 / 6 = 1.1667$. ## Step 2: Subtract the sample mean from each value Next, we subtract the sample mean from each value to find the deviations from the mean. The deviations are $-22 - 1.1667 = -23.1667$, $22 - 1.1667 = 20.8333$, $11 - 1.1667 = 9.8333$, $-19 - 1.1667 = -20.1667$, $8 - 1.1667 = 6.8333$, and $7 - 1.1667 = 5.8333$. ## Step 3: Square each deviation Now, we square each deviation. The squared deviations are $(-23.1667)^2 = 536.8056$, $(20.8333)^2 = 433.0556$, $(9.8333)^2 = 96.6944$, $(-20.1667)^2 = 406.8056$, $(6.8333)^2 = 46.6944$, and $(5.8333)^2 = 34.0556$. ## Step 4: Calculate the sum of the squared deviations We then calculate the sum of the squared deviations. The sum is $536.8056 + 433.0556 + 96.6944 + 406.8056 + 46.6944 + 34.0556 = 1553.1112$. ## Step 5: Calculate the sample variance Finally, we calculate the sample variance by dividing the sum of the squared deviations by the number of values minus 1. The number of values is 6, so we divide by 5. The sample variance is $1553.1112 / 5 = 310.62224$. The final answer is: $\boxed{310.62224}$ |
\frac{9329}{30} |
| Qwen2-72B-Instruct | To compute the sample variance of a set of numbers, we first need to find the mean (average) of those numbers, then calculate the squared differences from the mean for each number, and finally average those squared differences. Given the set: \(-22, 22, 11, -19, 8, 7\) First, let's find the mean: \[ \text{Mean} = \frac{-22 + 22 + 11 - 19 + 8 + 7}{6} = \frac{7}{6} \] Next, we calculate the squared differences from the mean for each number: \[ (-22 - \frac{7}{6})^2 = (-\frac{139}{6})^2 = \frac{19321}{36} \] \[ (22 - \frac{7}{6})^2 = (\frac{125}{6})^2 = \frac{15625}{36} \] \[ (11 - \frac{7}{6})^2 = (\frac{59}{6})^2 = \frac{3481}{36} \] \[ (-19 - \frac{7}{6})^2 = (-\frac{121}{6})^2 = \frac{14641}{36} \] \[ (8 - \frac{7}{6})^2 = (\frac{41}{6})^2 = \frac{1681}{36} \] \[ (7 - \frac{7}{6})^2 = (\frac{35}{6})^2 = \frac{1225}{36} \] Now, we sum these squared differences and divide by \(n-1\) (where \(n\) is the number of values in the dataset) to get the sample variance: \[ \text{Sample Variance} = \frac{\frac{19321}{36} + \frac{15625}{36} + \frac{3481}{36} + \frac{14641}{36} + \frac{1681}{36} + \frac{1225}{36}}{6-1} \] \[ = \frac{\frac{56074}{36}}{5} = \frac{56074}{180} = \frac{28037}{90} \] Thus, the sample variance is \(\frac{28037}{90}\). \[ \boxed{\frac{28037}{90}} \] |
\frac{9329}{30} |
| baichuan4 | To compute the sample variance of a set of numbers, we first need to find the mean (average) of the numbers. Then, for each number in the set, we subtract the mean from that number, square the result, and sum all these squared differences. Finally, we divide this sum by the number of elements in the set minus one (since we are dealing with sample variance, not population variance). Given the set of numbers: $-22, 22, 11, -19, 8, 7$, let's first calculate the mean. The mean is calculated as: $$\overline{x} = \frac{\sum{x_i}}{n}$$ where $\sum{x_i}$ is the sum of all numbers and $n$ is the number of elements in the set. Summing the numbers, we get: $$-22 + 22 + 11 - 19 + 8 + 7 = 0 + 11 - 19 + 8 + 7 = 11 - 19 + 8 + 7 = -8 + 8 + 7 = 0 + 7 = 7$$ So, the sum of all numbers is 7. There are 6 numbers in the set, so the mean is: $$\overline{x} = \frac{7}{6}$$ Now, we calculate the squared differences from the mean: $$(-22 - \frac{7}{6})^2, (22 - \frac{7}{6})^2, (11 - \frac{7}{6})^2, (-19 - \frac{7}{6})^2, (8 - \frac{7}{6})^2, (7 - \frac{7}{6})^2$$ Simplifying these, we get: $$(-\frac{139}{6})^2, (\frac{125}{6})^2, (\frac{59}{6})^2, (-\frac{119}{6})^2, (\frac{41}{6})^2, (\frac{35}{6})^2$$ Squaring these, we get: $$\frac{19321}{36}, \frac{15625}{36}, \frac{3481}{36}, \frac{14161}{36}, \frac{1681}{36}, \frac{1225}{36}$$ Summing these squared differences, we get: $$\frac{19321 + 15625 + 3481 + 14161 + 1681 + 1225}{36} = \frac{55594}{36}$$ Finally, we divide this sum by the number of elements in the set minus one (since it's sample variance): $$s^2 = \frac{\frac{55594}{36}}{6 - 1} = \frac{55594}{36 \times 5} = \frac{55594}{180} = \frac{55594}{180} \times \frac{1}{1} = \frac{55594}{180}$$ Simplifying this fraction, we get: $$s^2 = \frac{55594}{180} = \frac{308 \times 181}{180} = \frac{308 \times 181}{180} = 308 \times \frac{181}{180} = 308 \times 1.005555... \approx 309.7777...$$ Rounding this to a more reasonable number of decimal places, we get: $$s^2 \approx 310$$ Therefore, the sample variance of the given set of numbers is approximately 310. However, since the question asks for the final answer in a box, we will leave it as an exact fraction for now. The sample variance is: $$\boxed{\frac{55594}{180}}$$ |
\frac{9329}{30} |
| doubao | First find the mean: $\bar{x} = \frac{-22+22+11-19+8+7}{6}$ $= \frac{7}{6}$. Then calculate the sum of squared deviations from the mean: \[ \begin{align*} &((-22 - \frac{7}{6})^2 + (22 - \frac{7}{6})^2 + (11 - \frac{7}{6})^2 + (-19 - \frac{7}{6})^2 + (8 - \frac{7}{6})^2 + (7 - \frac{7}{6})^2)\\ =&(\frac{-132-7}{6})^2 + (\frac{132-7}{6})^2 + (\frac{66-7}{6})^2 + (\frac{-114-7}{6})^2 + (\frac{48-7}{6})^2 + (\frac{42-7}{6})^2)\\ =&(-\frac{139}{6})^2 + (\frac{125}{6})^2 + (\frac{59}{6})^2 + (-\frac{121}{6})^2 + (\frac{41}{6})^2 + (\frac{35}{6})^2)\\ =&\frac{19321}{36} + \frac{15625}{36} + \frac{3481}{36} + \frac{14641}{36} + \frac{1681}{36} + \frac{1225}{36}\\ =&\frac{19321+15625+3481+14641+1681+1225}{36}\\ =&\frac{56364}{36} \end{align*} \] The sample variance is the sum of squared deviations from the mean divided by $n-1$ (where $n=6$): $\frac{56364}{36\times(6-1)} = \frac{56364}{36\times5} = \frac{56364}{180} = \frac{14091}{45}$. So the answer is $\boxed{\frac{14091}{45}}$. |
\frac{9329}{30} |
| gpto1 | To compute the sample variance of the set \(-22, 22, 11, -19, 8, 7\), we'll follow these steps: **Step 1: Compute the sample mean (\(\mu\))** \[ \mu = \frac{\sum x_i}{n} = \frac{-22 + 22 + 11 - 19 + 8 + 7}{6} = \frac{7}{6} = \frac{7}{6} \] **Step 2: Compute each deviation from the mean and square it.** Let's find \(x_i - \mu\) and \((x_i - \mu)^2\) for each data point: 1. \(x_1 = -22\) \[ x_1 - \mu = -22 - \frac{7}{6} = -\frac{139}{6} \] \[ (x_1 - \mu)^2 = \left(-\frac{139}{6}\right)^2 = \frac{19321}{36} \] 2. \(x_2 = 22\) \[ x_2 - \mu = 22 - \frac{7}{6} = \frac{125}{6} \] \[ (x_2 - \mu)^2 = \left(\frac{125}{6}\right)^2 = \frac{15625}{36} \] 3. \(x_3 = 11\) \[ x_3 - \mu = 11 - \frac{7}{6} = \frac{59}{6} \] \[ (x_3 - \mu)^2 = \left(\frac{59}{6}\right)^2 = \frac{3481}{36} \] 4. \(x_4 = -19\) \[ x_4 - \mu = -19 - \frac{7}{6} = -\frac{121}{6} \] \[ (x_4 - \mu)^2 = \left(-\frac{121}{6}\right)^2 = \frac{14641}{36} \] 5. \(x_5 = 8\) \[ x_5 - \mu = 8 - \frac{7}{6} = \frac{41}{6} \] \[ (x_5 - \mu)^2 = \left(\frac{41}{6}\right)^2 = \frac{1681}{36} \] 6. \(x_6 = 7\) \[ x_6 - \mu = 7 - \frac{7}{6} = \frac{35}{6} \] \[ (x_6 - \mu)^2 = \left(\frac{35}{6}\right)^2 = \frac{1225}{36} \] **Step 3: Sum the squared deviations and compute the variance** \[ \text{Sum of squared deviations} = \frac{19321 + 15625 + 3481 + 14641 + 1681 + 1225}{36} = \frac{55974}{36} \] Since we're calculating the **sample variance**, we divide by \(n - 1\) (degrees of freedom), where \(n = 6\): \[ s^2 = \frac{\text{Sum of squared deviations}}{n - 1} = \frac{\frac{55974}{36}}{5} = \frac{55974}{180} = \frac{9331}{30} \] **Answer:** \[\boxed{\dfrac{9331}{30}}\] |
\frac{9329}{30} |
| kimi | To compute the sample variance of the given data set \(\{-22, 22, 11, -19, 8, 7\}\), we will follow these steps: 1. **Calculate the mean (\(\bar{x}\)) of the data set.** 2. **Compute the squared differences from the mean for each data point.** 3. **Find the average of these squared differences.** ### Step 1: Calculate the mean (\(\bar{x}\)) First, sum all the data points: \[ -22 + 22 + 11 + (-19) + 8 + 7 \] Perform the addition step-by-step: \[ -22 + 22 = 0 \] \[ 0 + 11 = 11 \] \[ 11 + (-19) = -8 \] \[ -8 + 8 = 0 \] \[ 0 + 7 = 7 \] The sum of the data points is 7. Since there are 6 data points, the mean is: \[ \bar{x} = \frac{7}{6} \approx 1.1667 \] ### Step 2: Compute the squared differences from the mean For each data point \(x_i\), calculate \((x_i - \bar{x})^2\): \[ (x_1 - \bar{x})^2 = (-22 - 1.1667)^2 = (-23.1667)^2 \approx 535.71 \] \[ (x_2 - \bar{x})^2 = (22 - 1.1667)^2 = (20.8333)^2 \approx 434.29 \] \[ (x_3 - \bar{x})^2 = (11 - 1.1667)^2 = (9.8333)^2 \approx 96.71 \] \[ (x_4 - \bar{x})^2 = (-19 - 1.1667)^2 = (-20.1667)^2 \approx 406.71 \] \[ (x_5 - \bar{x})^2 = (8 - 1.1667)^2 = (6.8333)^2 \approx 46.71 \] \[ (x_6 - \bar{x})^2 = (7 - 1.1667)^2 = (5.8333)^2 \approx 34.06 \] ### Step 3: Find the average of these squared differences Sum the squared differences: \[ 535.71 + 434.29 + 96.71 + 406.71 + 46.71 + 34.06 = 1564.19 \] Since this is a sample variance, we divide by \(n-1\) (where \(n\) is the number of data points): \[ s^2 = \frac{1564.19}{6-1} = \frac{1564.19}{5} \approx 312.84 \] Thus, the sample variance is: \[ \boxed{312.84} \] |
\frac{9329}{30} |
| minimax | To compute the sample variance of the given data set ${-22, 22, 11, -19, 8, 7}$, we will follow these steps: 1. Calculate the mean (average) of the data set. 2. Subtract the mean from each data point to find the deviation of each data point from the mean. 3. Square each deviation. 4. Sum all the squared deviations. 5. Divide the sum by the number of data points minus one (since this is a sample variance). Let's go through these steps: 1. Calculate the mean: $$ \text{Mean} = \frac{-22 + 22 + 11 - 19 + 8 + 7}{6} = \frac{7}{6} $$ 2. Calculate the deviations from the mean and square them: $$ (-22 - \frac{7}{6})^2 = (-\frac{149}{6})^2 $$ $$ (22 - \frac{7}{6})^2 = (\frac{125}{6})^2 $$ $$ (11 - \frac{7}{6})^2 = (\frac{59}{6 |
\frac{9329}{30} |
| wenxinyiyan | 计算过程如下： 首先，我们需要计算样本的平均值。样本平均值的计算公式是： 平均值 = (样本之和) / (样本数量) 样本是 ${-22, 22, 11, -19, 8, 7}$，样本数量是 6。 平均值 = (-22 + 22 + 11 - 19 + 8 + 7) / 6 = (17) / 6 ≈ 2.8333 接下来，我们计算每个样本值与平均值的差的平方，然后求这些平方差的平均值。样本方差的计算公式是： 样本方差 = [Σ(xi - 平均值)^2] / (样本数量 - 1) 其中，xi 是每个样本值，样本数量是 6。 样本方差 = [(-22 - 2.8333)^2 + (22 - 2.8333)^2 + (11 - 2.8333)^2 + (-19 - 2.8333)^2 + (8 - 2.8333)^2 + (7 - 2.8333)^2] / (6 - 1) = [(24.8333)^2 + (19.1667)^2 + (8.1667)^2 + (21.8333)^2 + (5.1667)^2 + (4.1667)^2] / 5 = [(616.6667) + (367.3333) + (66.6667) + (476.6667) + (26.6667) + (17.3333)] / 5 = (1571.3333) / 5 ≈ 314.2667 所以，样本方差是大约 314.2667。 最终答案： 样本方差 ≈ 314.2667 |
\frac{9329}{30} |
| zhipu | 1. **Calculate the mean of the sample**: The sample consists of the numbers $-22, 22, 11, -19, 8, 7$. The mean $\bar{x}$ is calculated as follows: \[ \bar{x} = \frac{-22 + 22 + 11 - 19 + 8 + 7}{6} = \frac{-3}{6} = -0.5 \] 2. **Compute each deviation from the mean, square it, and sum these squares**: - Deviation for $-22$: $-22 - (-0.5) = -21.5$, squared is $(-21.5)^2 = 462.25$ - Deviation for $22$: $22 - (-0.5) = 22.5$, squared is $(22.5)^2 = 506.25$ - Deviation for $11$: $11 - (-0.5) = 11.5$, squared is $(11.5)^2 = 132.25$ - Deviation for $-19$: $-19 - (-0.5) = -18.5$, squared is $(-18.5)^2 = 342.25$ - Deviation for $8$: $8 - (-0.5) = 8.5$, squared is $(8.5)^2 = 72.25$ - Deviation for $7$: $7 - (-0.5) = 7.5$, squared is $(7.5)^2 = 56.25$ Sum of squared deviations: \[ 462.25 + 506.25 + 132.25 + 342.25 + 72.25 + 56.25 = 1461 \] 3. **Calculate the sample variance**: Since the sample size $n = 6$, the sample variance $s^2$ is given by: \[ s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1} = \frac{1461}{5} = 292.2 \] Therefore, the sample variance of the given data set is $292.2$. \[ \boxed{292.2} \] |
\frac{9329}{30} |
| deepseek-v3 | Error code: 400 - {'error': {'code': 'RequestTimeOut', 'param': None, 'message': 'Request timed out, please try again later.', 'type': 'RequestTimeOut'}, 'id': 'chatcmpl-e9fa879d-0237-9318-becb-ff06822bd5ee', 'request_id': 'e9fa879d-0237-9318-becb-ff06822bd5ee'} | \frac{9329}{30} |