MySQL 5.6

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select @@version;


@@version


5.6.47


DROP TABLE IF EXISTS `data`;

CREATE TABLE IF NOT EXISTS `data` (
  `name` VARCHAR(25),
  `age` INT,
  `date` DATE,
  `value` DECIMAL (3, 1)
);
INSERT INTO `data`
  (`name`, `age`, `date`, `value`)
VALUES
  ('John', 20, '2020-01-01', 5),
  ('Peter', 21, '2020-01-02', 6.5),
  ('John', 26, '2019-02-26', 1.8),
  ('John', 20, '2029-10-13', 0.7),
  ('Peter', 47, '2020-01-18', 11.3),
  ('Peter', 21, '2020-02-01', 41.7),
  ('John', 20, '2020-01-22', 4);
SELECT
  CONCAT(
    '{',
    GROUP_CONCAT(
      CONCAT(
        `der`.`name_age`,
        ': {',
        `der`.`date_value`,
        '}'
      )
      SEPARATOR ', '),
    '}'
  ) `json_result`
FROM (
  SELECT
    CONCAT(
      '"',
      `name`,
      ' (', `age`, ')"'
    ) `name_age`,
    GROUP_CONCAT(
      CONCAT(
        '["',
        `date`,
        '", ',
        `value`,
        ']'
      )
      SEPARATOR ', ') `date_value`
  FROM
    `data`
  GROUP BY
    `name`, `age`
) `der`;


json_result


{"John (20)": {["2020-01-01", 5.0], ["2029-10-13", 0.7], ["2020-01-22", 4.0]}, "John (26)": {["2019-02-26", 1.8]}, "Peter (21)": {["2020-01-02", 6.5], ["2020-02-01", 41.7]}, "Peter (47)": {["2020-01-18", 11.3]}}