Looping through mean, median & mode and to end the number guessing game

In line 12, from statistics import median, mean imports median and mean, but mode is not imported.

In line 26, if guessed_number < 1 or guessed_number > 30: the statement is false if the guessed number is between 11 and 30.

In line 40, attempts.append(attempts), the variable attempts is the number of guesses rather than a list. If you are trying to get a list of all the numbers guessed, you could set attempts = [] in line 19 and attempts.append(guessed_number) after the if block in lines 26 through 28.

In lines 46 through 48,

mean_attempts = mean(attempts)
mode_attempts = mode(attempts)
median_attempts = median(attempts)

the variable attempts is not defined, since these lines are not part of start_game. If attempts is meant to be the list of how many tries it took to guess the number, you could set attempts = [] outside the start_game function and before the while loop, and move lines 46 through 49 after line 55 (where the game can first be played).

In line 49, print("Your average score is {}, your median value is {} and your mode value is {}.".format(mean_attempts, mode_attempts, median_attempts) is missing a closing ). The order of the median and the mode are swapped between the format string and the values. It might be easier to read using an f-string: print(f"Your average score is {mean_attempts}, your median value is {median_attempts} and your mode value is {mode_attempts}.")

In line 54, if user_decision == "yes": the variable user_decision was not previously defined. Try changing it to if choice == "yes":.

In line 55, new_game = start_game() sets new_game to the number of tries it took to guess the number, but the value of new_game is never used. You could append the value in new_game to an array attempts to calculate averages by attempts.append(new_game) if attempts is previously defined outside of start_game.

In line 61, start_game() starts a new game after having said goodbye in line 57.