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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Instructions
Compute the sample statistics on the given data using numpy. Write the equation in LaTeX first and then complete the computation in Python second. You may refer to equations in other problems. For example, to compute sample variance you could refer to the sample mean computed in problem 1.
example
The sum of the data is
$$
\sum x_i = 16
$$
Note that your answer must appear in the Markdown cell and Python cell
Step1:  Data
Step2:  Problem 1
Compute the mean
The mean is given by
$$
\bar{x} = \frac{1}{N} \sum_i^N x_i = 11.82
$$
Step3:  Problem 2
Compute the sample standard deviation
Sample standard deviation is given by
Step4:  Problem 3
Compute the correlation of the original data with the given data below
The sample correlation is given by
$$
r = \frac{\sigma_{xy}}{\sigma_x\sigma_y}
$$
where $\sigma_x$ is the sample standard deviation defined above and the sample covariance, $\sigma_{xy}$ is
$$
  \sigma_{xy}= \frac{1}{N - 1} \sum_i^N (x - \bar{x})(y - \bar{y})
$$
In this case $r = 0.865$
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Python Code:
#example
example_data_do_not_use = [4,3,6,3]
print(sum(example_data_do_not_use))
Explanation: Instructions
Compute the sample statistics on the given data using numpy. Write the equation in LaTeX first and then complete the computation in Python second. You may refer to equations in other problems. For example, to compute sample variance you could refer to the sample mean computed in problem 1.
example
The sum of the data is
$$
\sum x_i = 16
$$
Note that your answer must appear in the Markdown cell and Python cell
End of explanation
data=[13,13,11,11,12,10,14,14,8,11,14,10,16,11,11,15,12,13,12,11,13,12,14,10,9,12,13,14,14,10,15,13,12,12,13,10,12,10,13,13,14,8,14,11,9,13,10,11,9,9,15,12,14,10,16,14,9,10,12,13,8,11,16,13,10,10,13,10,11,11,14,7,12,14,13,13,9,9,13,10,12,12,13,12,10,10,13,11,15,13,13,17,9,12,12,9,12,9,10,12]
Explanation: Data
End of explanation
np.mean(data)
Explanation: Problem 1
Compute the mean
The mean is given by
$$
\bar{x} = \frac{1}{N} \sum_i^N x_i = 11.82
$$
End of explanation
np.std(data, ddof=1)
Explanation: Problem 2
Compute the sample standard deviation
Sample standard deviation is given by:
$$
\sigma_x = \sqrt{\frac{1}{N - 1} \sum_x (x - \bar{x})^2}
$$
and is $\sigma_x = 2.04$
End of explanation
data2=[16,15,14,13,16,12,15,15,9,13,17,13,19,14,16,18,15,14,14,14,14,14,15,14,13,14,16,18,15,13,17,16,14,16,17,13,16,13,17,16,16,11,18,12,12,16,13,15,14,11,15,17,17,15,20,16,11,14,14,15,11,14,19,16,13,11,13,11,13,15,16,9,13,15,15,15,10,11,17,11,15,15,16,15,12,12,16,13,17,17,15,18,11,16,15,11,15,12,14,16]
### BEGIN SOLUTION
np.corrcoef(data, data2)
### END SOLUTION
Explanation: Problem 3
Compute the correlation of the original data with the given data below
The sample correlation is given by
$$
r = \frac{\sigma_{xy}}{\sigma_x\sigma_y}
$$
where $\sigma_x$ is the sample standard deviation defined above and the sample covariance, $\sigma_{xy}$ is
$$
  \sigma_{xy}= \frac{1}{N - 1} \sum_i^N (x - \bar{x})(y - \bar{y})
$$
In this case $r = 0.865$
End of explanation
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