| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | To compute the sample variance of the set \(\{-11, 9, 5, 15, -10, -15, 12, -25, -22\}\), we follow these steps: 1. **Calculate the mean (average) of the sample:** \[ \text{Mean} = \frac{-11 + 9 + 5 + 15 + -10 + -15 + 12 + -25 + -22}{9} \] First, sum the numbers: \[ -11 + 9 + 5 + 15 + -10 + -15 + 12 + -25 + -22 = -42 \] Then, divide by the number of elements (9): \[ \text{Mean} = \frac{-42}{9} = -4.67 \] 2. **Calculate the squared differences from the mean for each data point:** \[ \begin{aligned} (-11 - (-4.67))^2 &= (-11 + 4.67)^2 = (-6.33)^2 = 40.07 \\ (9 - (-4.67))^2 &= (9 + 4.67)^2 = 13.67^2 = 186.87 \\ (5 - (-4.67))^2 &= (5 + 4.67)^2 = 9.67^2 = 93.51 \\ (15 - (-4.67))^2 &= (15 + 4.67)^2 = 19.67^2 = 386.91 \\ (-10 - (-4.67))^2 &= (-10 + 4.67)^2 = (-5.33)^2 = 28.41 \\ (-15 - (-4.67))^2 &= (-15 + 4.67)^2 = (-10.33)^2 = 106.71 \\ (12 - (-4.67))^2 &= (12 + 4.67)^2 = 16.67^2 = 277.89 \\ (-25 - (-4.67))^2 &= (-25 + 4.67)^2 = (-20.33)^2 = 413.31 \\ (-22 - (-4.67))^2 &= (-22 + 4.67)^2 = (-17.33)^2 = 300.31 \\ \end{aligned} \] 3. **Sum the squared differences:** \[ \sum (x_i - \bar{x})^2 = 40.07 + 186.87 + 93.51 + 386.91 + 28.41 + 106.71 + 277.89 + 413.31 + 300.31 = 1834.00 \] 4. **Calculate the sample variance:** \[ \text{Sample Variance} = \frac{\sum (x_i - \bar{x})^2}{n - 1} = \frac{1834.00}{9 - 1} = \frac{1834.00}{8} = 229.25 \] Thus, the sample variance is: \[ \boxed{229.25} \] |
\frac{917}{4} |
| deepseek-r1 | To compute the sample variance of the data set \(\{-11, 9, 5, 15, -10, -15, 12, -25, -22\}\), we follow these steps: 1. **Calculate the mean**: \[ \text{Mean} = \frac{-11 + 9 + 5 + 15 - 10 - 15 + 12 - 25 - 22}{9} = \frac{-42}{9} = -\frac{14}{3} \] 2. **Compute the squared differences from the mean**: \[ \begin{align*} (-11 - (-\frac{14}{3}))^2 &= \left(-\frac{19}{3}\right)^2 = \frac{361}{9}, \\ (9 - (-\frac{14}{3}))^2 &= \left(\frac{41}{3}\right)^2 = \frac{1681}{9}, \\ (5 - (-\frac{14}{3}))^2 &= \left(\frac{29}{3}\right)^2 = \frac{841}{9}, \\ (15 - (-\frac{14}{3}))^2 &= \left(\frac{59}{3}\right)^2 = \frac{3481}{9}, \\ (-10 - (-\frac{14}{3}))^2 &= \left(-\frac{16}{3}\right)^2 = \frac{256}{9}, \\ (-15 - (-\frac{14}{3}))^2 &= \left(-\frac{31}{3}\right)^2 = \frac{961}{9}, \\ (12 - (-\frac{14}{3}))^2 &= \left(\frac{50}{3}\right)^2 = \frac{2500}{9}, \\ (-25 - (-\frac{14}{3}))^2 &= \left(-\frac{61}{3}\right)^2 = \frac{3721}{9}, \\ (-22 - (-\frac{14}{3}))^2 &= \left(-\frac{52}{3}\right)^2 = \frac{2704}{9}. \end{align*} \] 3. **Sum the squared differences**: \[ \frac{361 + 1681 + 841 + 3481 + 256 + 961 + 2500 + 3721 + 2704}{9} = \frac{16506}{9} = 1834 \] 4. **Divide by \(n-1\) (where \(n = 9\))**: \[ \text{Sample Variance} = \frac{1834}{8} = 229.25 \] Thus, the sample variance is \(\boxed{229.25}\). |
\frac{917}{4} |
| gpto1 | To compute the sample variance \( s^2 \) of the given data set: \[ {-11,\ 9,\ 5,\ 15,\ -10,\ -15,\ 12,\ -25,\ -22} \] **Step 1: Calculate the sample mean \( \bar{x} \).** Sum all the data points: \[ \text{Sum} = (-11) + 9 + 5 + 15 + (-10) + (-15) + 12 + (-25) + (-22) = -42 \] Divide by the number of data points (\( n = 9 \)): \[ \bar{x} = \frac{-42}{9} = -\frac{14}{3} \] **Step 2: Compute each squared deviation \((x_i - \bar{x})^2\).** For each data point \( x_i \): 1. \( x_1 = -11 \) \( x_1 - \bar{x} = -11 + \frac{14}{3} = -\frac{19}{3} \) \((x_1 - \bar{x})^2 = \left(-\frac{19}{3}\right)^2 = \frac{361}{9}\) 2. \( x_2 = 9 \) \( x_2 - \bar{x} = 9 + \frac{14}{3} = \frac{41}{3} \) \((x_2 - \bar{x})^2 = \left(\frac{41}{3}\right)^2 = \frac{1681}{9}\) 3. Continuing similarly for all data points, we find: \[ \begin{align*} (x_3 - \bar{x})^2 &= \frac{841}{9} \\ (x_4 - \bar{x})^2 &= \frac{3481}{9} \\ (x_5 - \bar{x})^2 &= \frac{256}{9} \\ (x_6 - \bar{x})^2 &= \frac{961}{9} \\ (x_7 - \bar{x})^2 &= \frac{2500}{9} \\ (x_8 - \bar{x})^2 &= \frac{3721}{9} \\ (x_9 - \bar{x})^2 &= \frac{2704}{9} \end{align*} \] **Step 3: Sum the squared deviations and compute the variance.** Sum all the squared deviations: \[ \sum (x_i - \bar{x})^2 = \frac{361 + 1681 + 841 + 3481 + 256 + 961 + 2500 + 3721 + 2704}{9} = \frac{16506}{9} \] Compute the sample variance: \[ s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1} = \frac{\frac{16506}{9}}{8} = \frac{1834}{8} = \frac{917}{4} \] **Final Answer:** \[ \boxed{\dfrac{917}{4}} \] $\boxed{\dfrac{917}{4}}$ |
\frac{917}{4} |
| gpt-4o-2024-08-06 | To compute the sample variance, we follow these steps: 1. **Calculate the sample mean**: \[ \bar{x} = \frac{-11 + 9 + 5 + 15 - 10 - 15 + 12 - 25 - 22}{9} \] First, compute the sum of the data: \[ -11 + 9 + 5 + 15 - 10 - 15 + 12 - 25 - 22 = -42 \] Now, divide by the number of data points (9): \[ \bar{x} = \frac{-42}{9} = -\frac{42}{9} = -4.6667 \] 2. **Calculate the squared deviations from the mean**: \[ \begin{align*} (-11 - (-4.6667))^2 & = (-11 + 4.6667)^2 = (-6.3333)^2 = 40.1111, \\ (9 - (-4.6667))^2 & = (9 + 4.6667)^2 = 13.6667^2 = 186.7778, \\ (5 - (-4.6667))^2 & = (5 + 4.6667)^2 = 9.6667^2 = 93.4444, \\ (15 - (-4.6667))^2 & = (15 + 4.6667)^2 = 19.6667^2 = 386.7778, \\ (-10 - (-4.6667))^2 & = (-10 + 4.6667)^2 = (-5.3333)^2 = 28.4444, \\ (-15 - (-4.6667))^2 & = (-15 + 4.6667)^2 = (-10.3333)^2 = 106.7778, \\ (12 - (-4.6667))^2 & = (12 + 4.6667)^2 = 16.6667^2 = 277.7778, \\ (-25 - (-4.6667))^2 & = (-25 + 4.6667)^2 = (-20.3333)^2 = 413.4444, \\ (-22 - (-4.6667))^2 & = (-22 + 4.6667)^2 = (-17.3333)^2 = 300.4444. \end{align*} \] 3. **Sum the squared deviations**: \[ 40.1111 + 186.7778 + 93.4444 + 386.7778 + 28.4444 + 106.7778 + 277.7778 + 413.4444 + 300.4444 = 1834.0 \] 4. **Divide by \( n - 1 \) to get the sample variance**: \[ s^2 = \frac{1834.0}{9 - 1} = \frac{1834.0}{8} = 229.25 \] Thus, the sample variance is \(\boxed{229.25}\). |
\frac{917}{4} |
| DeepSeek-Coder-V2-Lite-Instruct | To compute the sample variance of the given list of numbers, we will follow these steps: 1. **Calculate the mean (average) of the numbers.** 2. **Find the squared differences between each number and the mean.** 3. **Sum these squared differences.** 4. **Divide the sum by the number of elements minus one (n-1).** Let's go through these steps in detail: ### Step 1: Calculate the mean The given list of numbers is: \({-11, 9, 5, 15, -10, -15, 12, -25, -22}\) First, sum all the numbers: \[ -11 + 9 + 5 + 15 - 10 - 15 + 12 - 25 - 22 \] Let's add them step by step: \[ -11 + 9 = -2 \] \[ -2 + 5 = 3 \] \[ 3 + 15 = 18 \] \[ 18 - 10 = 8 \] \[ 8 - 15 = -7 \] \[ -7 + 12 = 5 \] \[ 5 - 25 = -20 \] \[ -20 - 22 = -42 \] The sum of the numbers is \(-42\). There are 9 numbers, so the mean is: \[ \text{Mean} = \frac{-42}{9} = -4.6667 \] ### Step 2: Find the squared differences Now, we calculate the squared difference between each number and the mean \(-4.6667\): 1. For \(-11\): \[ (-11 - (-4.6667))^2 = (-11 + 4.6667)^2 = (-6.3333)^2 = 40.1111 \] 2. For \(9\): \[ (9 - (-4.6667))^2 = (9 + 4.6667)^2 = 13.6667^2 = 186.7778 \] 3. For \(5\): \[ (5 - (-4.6667))^2 = (5 + 4.6667)^2 = 9.6667^2 = 93.4444 \] 4. For \(15\): \[ (15 - (-4.6667))^2 = (15 + 4.6667)^2 = 19.6667^2 = 386.7778 \] 5. For \(-10\): \[ (-10 - (-4.6667))^2 = (-10 + 4.6667)^2 = -5.3333^2 = 28.4444 \] 6. For \(-15\): \[ (-15 - (-4.6667))^2 = (-15 + 4.6667)^2 = -10.3333^2 = 106.7778 \] 7. For \(12\): \[ (12 - (-4.6667))^2 = (12 + 4.6667)^2 = 16.6667^2 = 277.7778 \] 8. For \(-25\): \[ (-25 - (-4.6667))^2 = (-25 + 4.6667)^2 = -20.3333^2 = 413.4444 \] 9. For \(-22\): \[ (-22 - (-4.6667))^2 = (-22 + 4.6667)^2 = -17.3333^2 = 300.4444 \] ### Step 3: Sum these squared differences \[ 40.1111 + 186.7778 + 93.4444 + 386.7778 + 28.4444 + 106.7778 + 277.7778 + 413.4444 + 300.4444 \] Let's add them step by step: \[ 40.1111 + 186.7778 = 226.8889 \] \[ 226.8889 + 93.4444 = 320.3333 \] \[ 320.3333 + 386.7778 = 707.1111 \] \[ 707.1111 + 28.4444 = 735.5555 \] \[ 735.5555 + 106.7778 = 842.3333 \] \[ 842.3333 + 277.7778 = 1120.1111 \] \[ 1120.1111 + 413.4444 = 1533.5555 \] \[ 1533.5555 + 300.4444 = 1834 \] ### Step 4: Divide the sum by the number of elements minus one (n-1) \[ \text{Sample Variance} = \frac{1834}{9 - 1} = \frac{1834}{8} = 229.25 \] Thus, the sample variance is: \[ \boxed{229.25} \] |
\frac{917}{4} |
| 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. We add up all the numbers and then divide by the total count of numbers. ## Step 2: Add up all the numbers in the dataset The sum of all the numbers in the dataset is: -11 + 9 + 5 + 15 - 10 - 15 + 12 - 25 - 22 = -42. ## Step 3: Calculate the sample mean There are 9 numbers in the dataset. The sample mean is the sum of all the numbers divided by the count of numbers, which is -42 / 9 = -4.67. ## Step 4: Calculate the deviations from the mean Next, we need to find the deviations of each number from the sample mean. This is done by subtracting the sample mean from each number. ## Step 5: Calculate the squared deviations After finding the deviations, we need to square each deviation. This is done by multiplying each deviation by itself. ## Step 6: Calculate the sum of the squared deviations Now, we add up all the squared deviations. (-11 - (-4.67))^2 + (9 - (-4.67))^2 + (5 - (-4.67))^2 + (15 - (-4.67))^2 + (-10 - (-4.67))^2 + (-15 - (-4.67))^2 + (12 - (-4.67))^2 + (-25 - (-4.67))^2 + (-22 - (-4.67))^2 = (-6.33)^2 + (13.67)^2 + (9.67)^2 + (19.67)^2 + (-5.33)^2 + (-10.33)^2 + (16.67)^2 + (-20.33)^2 + (-17.33)^2 = 40.07 + 186.95 + 93.45 + 386.95 + 28.41 + 106.69 + 278.69 + 413.41 + 300.25 = 1834.87 ## Step 7: Calculate the sample variance Finally, we calculate the sample variance by dividing the sum of the squared deviations by the count of numbers minus one (n-1). In this case, n-1 = 9-1 = 8. Sample variance = 1834.87 / 8 = 229.36. The final answer is: $\boxed{229.36}$ |
\frac{917}{4} |
| 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 given values are ${-11, 9, 5, 15, -10, -15, 12, -25, -22}$. The sum of these values is $-11 + 9 + 5 + 15 - 10 - 15 + 12 - 25 - 22 = -42$. There are 9 values in the sample. Therefore, the sample mean is $-42 / 9 = -4.67$. ## Step 2: Calculate the deviations from the mean Next, we need to calculate the deviations from the mean for each value. This is done by subtracting the sample mean from each value. The deviations are $(-11 - (-4.67))$, $(9 - (-4.67))$, $(5 - (-4.67))$, $(15 - (-4.67))$, $(-10 - (-4.67))$, $(-15 - (-4.67))$, $(12 - (-4.67))$, $(-25 - (-4.67))$, $(-22 - (-4.67))$. ## Step 3: Calculate the squared deviations Now, we calculate the squared deviations by squaring each deviation. The squared deviations are $(-11 + 4.67)^2$, $(9 + 4.67)^2$, $(5 + 4.67)^2$, $(15 + 4.67)^2$, $(-10 + 4.67)^2$, $(-15 + 4.67)^2$, $(12 + 4.67)^2$, $(-25 + 4.67)^2$, $(-22 + 4.67)^2$. ## Step 4: Calculate the sum of the squared deviations We then calculate the sum of the squared deviations. This is $(-6.33)^2 + (13.67)^2 + (9.67)^2 + (19.67)^2 + (-5.33)^2 + (-10.33)^2 + (16.67)^2 + (-20.33)^2 + (-17.33)^2$. ## Step 5: Calculate the sum of the squared deviations Now, we calculate the sum of the squared deviations. This is $40.07 + 186.89 + 93.45 + 388.09 + 28.41 + 106.69 + 277.89 + 412.41 + 299.69$. ## Step 6: Calculate the sum of the squared deviations Now, we calculate the sum of the squared deviations. This is $40.07 + 186.89 + 93.45 + 388.09 + 28.41 + 106.69 + 277.89 + 412.41 + 299.69 = 1833.09$. ## Step 7: Calculate the sample variance The sample variance is calculated by dividing the sum of the squared deviations by the number of values minus 1. In this case, we divide by 8. Therefore, the sample variance is $1833.09 / 8 = 229.14$. The final answer is: $\boxed{229.14}$ |
\frac{917}{4} |
| 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: \(-11, 9, 5, 15, -10, -15, 12, -25, -22\) First, let's find the mean: \[ \text{Mean} = \frac{-11 + 9 + 5 + 15 + (-10) + (-15) + 12 + (-25) + (-22)}{9} \] \[ = \frac{-47}{9} \] \[ = -5.2222... \] Next, we calculate the squared differences from the mean for each number: \[ (-11 - (-5.2222))^2 = 34.6944 \] \[ (9 - (-5.2222))^2 = 186.6944 \] \[ (5 - (-5.2222))^2 = 104.6944 \] \[ (15 - (-5.2222))^2 = 363.6944 \] \[ (-10 - (-5.2222))^2 = 21.6944 \] \[ (-15 - (-5.2222))^2 = 94.6944 \] \[ (12 - (-5.2222))^2 = 299.6944 \] \[ (-25 - (-5.2222))^2 = 394.6944 \] \[ (-22 - (-5.2222))^2 = 234.6944 \] Now, we sum these squared differences and divide by \(n-1\) (where \(n\) is the number of data points) to get the sample variance: \[ \text{Sample Variance} = \frac{34.6944 + 186.6944 + 104.6944 + 363.6944 + 21.6944 + 94.6944 + 299.6944 + 394.6944 + 234.6944}{9-1} \] \[ = \frac{1730.76}{8} \] \[ = 216.345 \] Therefore, the sample variance of the given set is approximately \(216.345\). \[ \boxed{216.345} \] |
\frac{917}{4} |
| baichuan4 | To compute the sample variance of a set of numbers, we first need to calculate mean (average 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: $$-11, 9, 5, 15, -10, -15, 12, -25, -22$$ First, we calculate the mean: $$\overline{x} = \frac{-11 + 9 + 5 + 15 - 10 - 15 + 12 - 25 - 22}{9} = \frac{-42}{9} = -4.67$$ Next, we compute the sum of squared differences from the mean: $$\sum (x_i - \overline{x})^2 = (-11 - (-4.67))^2 + (9 - (-4.67))^2 + (5 - (-4.67))^2 + (15 - (-4.67))^2 + (-10 - (-4.67))^2 + (-15 - (-4.67))^2 + (12 - (-4.67))^2 + (-25 - (-4.67))^2 + (-22 - (-4.67))^2$$ $$= (-6.33)^2 + (13.67)^2 + (9.67)^2 + (19.67)^2 + (-5.33)^2 + (-10.33)^2 + (16.67)^2 + (-20.33)^2 + (-17.33)^2$$ $$= 40.0889 + 186.7189 + 93.4989 + 386.8889 + 28.4389 + 106.7189 + 277.8889 + 413.2889 + 299.9889$$ $$= 1833.4211$$ Finally, we divide this sum by the number of elements in the set minus one (since it's sample variance): $$s^2 = \frac{\sum (x_i - \overline{x})^2}{n - 1} = \frac{1833.4211}{9 - 1} = \frac{1833.4211}{8} = 229.1776$$ So, the sample variance is approximately: $$s^2 \approx 229.1776$$ Putting the final answer in a box, we have: $$\boxed{229.1776}$$ |
\frac{917}{4} |
| doubao | Detailed exception information is listed below. req_id: 20241010114252000032621F2B7850BC8C code_n: 1709701 code: ClientSDKRequestError message: MaaS SDK request error: HTTPSConnectionPool(host='maas-api.ml-platform-cn-beijing.volces.com', port=443): Read timed out. (read timeout=60) |
\frac{917}{4} |
| gpto1 | To compute the sample variance \( s^2 \) of the given data set: \[ {-11,\ 9,\ 5,\ 15,\ -10,\ -15,\ 12,\ -25,\ -22} \] **Step 1: Calculate the sample mean \( \bar{x} \).** Sum all the data points: \[ \text{Sum} = (-11) + 9 + 5 + 15 + (-10) + (-15) + 12 + (-25) + (-22) = -42 \] Divide by the number of data points (\( n = 9 \)): \[ \bar{x} = \frac{-42}{9} = -\frac{14}{3} \] **Step 2: Compute each squared deviation \((x_i - \bar{x})^2\).** For each data point \( x_i \): 1. \( x_1 = -11 \) \( x_1 - \bar{x} = -11 + \frac{14}{3} = -\frac{19}{3} \) \((x_1 - \bar{x})^2 = \left(-\frac{19}{3}\right)^2 = \frac{361}{9}\) 2. \( x_2 = 9 \) \( x_2 - \bar{x} = 9 + \frac{14}{3} = \frac{41}{3} \) \((x_2 - \bar{x})^2 = \left(\frac{41}{3}\right)^2 = \frac{1681}{9}\) 3. Continuing similarly for all data points, we find: \[ \begin{align*} (x_3 - \bar{x})^2 &= \frac{841}{9} \\ (x_4 - \bar{x})^2 &= \frac{3481}{9} \\ (x_5 - \bar{x})^2 &= \frac{256}{9} \\ (x_6 - \bar{x})^2 &= \frac{961}{9} \\ (x_7 - \bar{x})^2 &= \frac{2500}{9} \\ (x_8 - \bar{x})^2 &= \frac{3721}{9} \\ (x_9 - \bar{x})^2 &= \frac{2704}{9} \end{align*} \] **Step 3: Sum the squared deviations and compute the variance.** Sum all the squared deviations: \[ \sum (x_i - \bar{x})^2 = \frac{361 + 1681 + 841 + 3481 + 256 + 961 + 2500 + 3721 + 2704}{9} = \frac{16506}{9} \] Compute the sample variance: \[ s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1} = \frac{\frac{16506}{9}}{8} = \frac{1834}{8} = \frac{917}{4} \] **Final Answer:** \[ \boxed{\dfrac{917}{4}} \] $\boxed{\dfrac{917}{4}}$ |
\frac{917}{4} |
| kimi | First, calculate the mean of the data set: $$\text{Mean} = \frac{-11 + 9 + 5 + 15 - 10 - 15 + 12 - 25 - 22}{9} = \frac{-41}{9}.$$ Next, compute the squared differences from the mean and sum them up: \begin{align*} &\left(-11 - \frac{-41}{9}\right)^2 + \left(9 - \frac{-41}{9}\right)^2 + \left(5 - \frac{-41}{9}\right)^2 + \left(15 - \frac{-41}{9}\right)^2 \\ &+ \left(-10 - \frac{-41}{9}\right)^2 + \left(-15 - \frac{-41}{9}\right)^2 + \left(12 - \frac{-41}{9}\right)^2 + \left(-25 - \frac{-41}{9}\right)^2 + \left(-22 - \frac{-41}{9}\right)^2 \\ &= \left(\frac{-80}{9}\right)^2 + \left(\frac{130}{9}\right)^2 + \left(\frac{76}{9}\right)^2 + \left(\frac{196}{9}\right)^2 \\ &+ \left(\frac{51}{9}\right)^2 + \left(\frac{-76}{9}\right)^2 + \left(\frac{163}{9}\right)^2 + \left(\frac{-166}{9}\right)^2 + \left(\frac{-151}{9}\right)^2 \\ &= \frac{6400}{81} + \frac{16900}{81} + \frac{5776}{81} + \frac{38416}{81} + \frac{2601}{81} + \frac{5776}{81} + \frac{26569}{81} + \frac{27556}{81} + \frac{22801}{81}. \end{align*} Summing these values: $$\frac{6400 + 16900 + 5776 + 38416 + 2601 + 5776 + 26569 + 27556 + 22801}{81} = \frac{142429}{81}.$$ Finally, divide by the number of data points minus one to find the variance: $$\text{Variance} = \frac{142429}{81 \times 8} = \frac{142429}{648}.$$ Thus, the sample variance is $\boxed{\frac{142429}{648}}$. |
\frac{917}{4} |
| minimax | To compute the sample variance of the given data set, we will follow these steps: 1. Find 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 with the given data set: {-11, 9, 5, 15, -10, -15, 12, -25, -22}. Step 1: Calculate the mean. Mean = (sum of all data points) / (number of data points) Mean = (-11 + 9 + 5 + 15 - 10 - 15 + 12 - 25 - 22) / 9 Mean = (-62) / 9 Mean = -62 / 9 Mean ≈ -6.89 Step 2: Calculate the deviation of each data point from the mean and then square it. Deviation squared for -11: (-11 - |
\frac{917}{4} |
| wenxinyiyan | 首先，我们需要计算给定数据集${-11, 9, 5, 15, -10, -15, 12, -25, -22}$的均值。 均值是所有数据之和除以数据的数量。 均值 $= \frac{-11 + 9 + 5 + 15 - 10 - 15 + 12 - 25 - 22}{9} = \frac{-42}{9} = -4.6667$ 接下来，我们计算每个数据与均值的差的平方。 $(-11 + 4.6667)^2 = 40.4444$ $(9 + 4.6667)^2 = 190.4444$ $(5 + 4.6667)^2 = 94.2222$ $(15 + 4.6667)^2 = 382.2222$ $(-10 + 4.6667)^2 = 28.4444$ $(-15 + 4.6667)^2 = 106.2222$ $(12 + 4.6667)^2 = 278.2222$ $(-25 + 4.6667)^2 = 412.4444$ $(-22 + 4.6667)^2 = 302.2222$ 然后，我们计算这些平方差的均值。 $\frac{40.4444 + 190.4444 + 94.2222 + 382.2222 + 28.4444 + 106.2222 + 278.2222 + 412.4444 + 302.2222}{9} = 174.2222$ 所以，给定数据集的样本方差为$\boxed{174.2222}$。 |
\frac{917}{4} |
| zhipu | To compute the sample variance of the data set \(\{-11, 9, 5, 15, -10, -15, 12, -25, -22\}\), follow these steps: 1. **Calculate the sample mean (\(\bar{x}\))**: \[ \bar{x} = \frac{\sum_{i=1}^{n} x_i}{n} \] where \(n\) is the number of data points. First, sum all the data points: \[ -11 + 9 + 5 + 15 - 10 - 15 + 12 - 25 - 22 = -52 \] There are 9 data points, so: \[ \bar{x} = \frac{-52}{9} \approx -5.78 \] 2. **Calculate the squared deviations from the mean**: For each data point \(x_i\), compute \((x_i - \bar{x})^2\): \[ \begin{align*} (-11 - (-5.78))^2 & = (-11 + 5.78)^2 = (-5.22)^2 = 27.2484 \\ (9 - (-5.78))^2 & = (9 + 5.78)^2 = 14.78^2 = 217.2324 \\ (5 - (-5.78))^2 & = (5 + 5.78)^2 = 10.78^2 = 116.3284 \\ (15 - (-5.78))^2 & = (15 + 5.78)^2 = 20.78^2 = 431.8284 \\ (-10 - (-5.78))^2 & = (-10 + 5.78)^2 = (-4.22)^2 = 17.9584 \\ (-15 - (-5.78))^2 & = (-15 + 5.78)^2 = (-9.22)^2 = 85.0284 \\ (12 - (-5.78))^2 & = (12 + 5.78)^2 = 17.78^2 = 316.1844 \\ (-25 - (-5.78))^2 & = (-25 + 5.78)^2 = (-19.22)^2 = 368.6884 \\ (-22 - (-5.78))^2 & = (-22 + 5.78)^2 = (-16.22)^2 = 262.1284 \\ \end{align*} \] 3. **Sum the squared deviations**: \[ 27.2484 + 217.2324 + 116.3284 + 431.8284 + 17.9584 + 85.0284 + 316.1844 + 368.6884 + 262.1284 = 1782.194 \] 4. **Calculate the sample variance (\(s^2\))**: The formula for sample variance is: \[ s^2 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n - 1} \] With \(n = 9\): \[ s^2 = \frac{1782.194}{9 - 1} = \frac{1782.194}{8} \approx 223.02425 \] Thus, the sample variance is \(\boxed{223.02425}\). |
\frac{917}{4} |
| deepseek-v3 | Error code: 400 - {'error': {'code': 'RequestTimeOut', 'param': None, 'message': 'Request timed out, please try again later.', 'type': 'RequestTimeOut'}, 'id': 'chatcmpl-a190e4df-b428-9a81-84d5-f6bb692efff4', 'request_id': 'a190e4df-b428-9a81-84d5-f6bb692efff4'} | \frac{917}{4} |