import math
class Statistics3:
    """
    This is a class that implements methods for calculating indicators such as median, mode, correlation matrix, and Z-score in statistics.
    """
    @staticmethod
    def median(data):
        """
        calculates the median of the given list.
        :param data: the given list, list.
        :return: the median of the given list, float.
        >>> statistics3 = Statistics3()
        >>> statistics3.median([1, 2, 3, 4])
        2.5

        """

        sorted_data = sorted(data)
        n = len(sorted_data)
        if n % 2 == 1:
            return sorted_data[n // 2]
        else:
            return (sorted_data[n // 2 - 1] + sorted_data[n // 2]) / 2

    @staticmethod
    def mode(data):
        """
        calculates the mode of the given list.
        :param data: the given list, list.
        :return: the mode of the given list, list.
        >>> statistics3 = Statistics3()
        >>> statistics3.mode([1, 2, 3, 3])
        [3]

        """

        counts = {}
        for value in data:
            counts[value] = counts.get(value, 0) + 1
        max_count = max(counts.values())
        mode_values = [value for value, count in counts.items() if count == max_count]
        return mode_values

    @staticmethod
    def mean(data):
        """
        calculates the mean of the given list.
        :param data: the given list, list.
        :return: the mean of the given list, float.
        >>> statistics3 = Statistics3()
        >>> statistics3.mean([1, 2, 3])
        2.0

        """

        if len(data) == 0:
            return None
        return sum(data) / len(data)

    @staticmethod
    def correlation_matrix(data):
        """
        calculates the correlation matrix of the given list.
        :param data: the given list, list.
        :return: the correlation matrix of the given list, list.
        >>> statistics3 = Statistics3()
        >>> statistics3.correlation_matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
        [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]

        """

        matrix = []
        for i in range(len(data[0])):
            row = []
            for j in range(len(data[0])):
                column1 = [row[i] for row in data]
                column2 = [row[j] for row in data]
                correlation = Statistics3.correlation(column1, column2)
                row.append(correlation)
            matrix.append(row)
        return matrix

    @staticmethod
    def standard_deviation(data):
        """
        calculates the standard deviation of the given list.
        :param data: the given list, list.
        :return: the standard deviation of the given list, float.
        >>> statistics3 = Statistics3()
        >>> statistics3.standard_deviation([1, 2, 3])
        1.0

        """

        n = len(data)
        if n < 2:
            return None
        mean_value = Statistics3.mean(data)
        variance = sum((x - mean_value) ** 2 for x in data) / (n - 1)
        return math.sqrt(variance)

    @staticmethod
    def z_score(data):
        """
        calculates the z-score of the given list.
        :param data: the given list, list.
        :return: the z-score of the given list, list.
        >>> statistics3 = Statistics3()
        >>> statistics3.z_score([1, 2, 3, 4])
        [-1.161895003862225, -0.3872983346207417, 0.3872983346207417, 1.161895003862225]

        """

        mean = Statistics3.mean(data)
        std_deviation = Statistics3.standard_deviation(data)
        if std_deviation is None or std_deviation == 0:
            return None
        return [(x - mean) / std_deviation for x in data]

Method:
@staticmethod
    def correlation(x, y):
        n = len(x)
        mean_x = sum(x) / n
        mean_y = sum(y) / n
        numerator = sum((xi - mean_x) * (yi - mean_y) for xi, yi in zip(x, y))
        denominator = math.sqrt(sum((xi - mean_x) ** 2 for xi in x) * sum((yi - mean_y) ** 2 for yi in y))
        if denominator == 0:
            return None
        return numerator / denominator

Summary: calculates the correlation of the given list.