Nonempty Observation List Descriptive Statistics Foundations

0/1

Sum all 1 observations with their multiplicities and divide by that positive count, obtaining 0/1. Do not average a deduplicated set or infer a population probability law.

-3/1

Sum all 3 observations with their multiplicities and divide by that positive count, obtaining -3/1. Do not average a deduplicated set or infer a population probability law.

5/3

Sum all 3 observations with their multiplicities and divide by that positive count, obtaining 5/3. Do not average a deduplicated set or infer a population probability law.

3/2

Sum all 4 observations with their multiplicities and divide by that positive count, obtaining 3/2. Do not average a deduplicated set or infer a population probability law.

4/5

Sum all 5 observations with their multiplicities and divide by that positive count, obtaining 4/5. Do not average a deduplicated set or infer a population probability law.

-2/3

Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -2/3. Do not average a deduplicated set or infer a population probability law.

17/6

Sum all 6 observations with their multiplicities and divide by that positive count, obtaining 17/6. Do not average a deduplicated set or infer a population probability law.

-4/3

Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -4/3. Do not average a deduplicated set or infer a population probability law.

-7/6

Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -7/6. Do not average a deduplicated set or infer a population probability law.

23/6

Sum all 6 observations with their multiplicities and divide by that positive count, obtaining 23/6. Do not average a deduplicated set or infer a population probability law.

-11/6

Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -11/6. Do not average a deduplicated set or infer a population probability law.

-5/3

Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -5/3. Do not average a deduplicated set or infer a population probability law.

29/6

Sum all 6 observations with their multiplicities and divide by that positive count, obtaining 29/6. Do not average a deduplicated set or infer a population probability law.

-7/3

Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -7/3. Do not average a deduplicated set or infer a population probability law.

-13/6

Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -13/6. Do not average a deduplicated set or infer a population probability law.

35/6

Sum all 6 observations with their multiplicities and divide by that positive count, obtaining 35/6. Do not average a deduplicated set or infer a population probability law.

-17/6

Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -17/6. Do not average a deduplicated set or infer a population probability law.

-8/3

Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -8/3. Do not average a deduplicated set or infer a population probability law.

41/6

Sum all 6 observations with their multiplicities and divide by that positive count, obtaining 41/6. Do not average a deduplicated set or infer a population probability law.

-10/3

Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -10/3. Do not average a deduplicated set or infer a population probability law.

-19/6

Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -19/6. Do not average a deduplicated set or infer a population probability law.

47/6

Sum all 6 observations with their multiplicities and divide by that positive count, obtaining 47/6. Do not average a deduplicated set or infer a population probability law.

-23/6

Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -23/6. Do not average a deduplicated set or infer a population probability law.

-11/3

Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -11/3. Do not average a deduplicated set or infer a population probability law.

53/6

Sum all 6 observations with their multiplicities and divide by that positive count, obtaining 53/6. Do not average a deduplicated set or infer a population probability law.

0/1

The sorted list retaining repetitions is [0]. Apply the stated odd/even convention to obtain 0/1; the even-length median need not be an observed value.

-3/1

The sorted list retaining repetitions is [-3, -3, -3]. Apply the stated odd/even convention to obtain -3/1; the even-length median need not be an observed value.

1/1

The sorted list retaining repetitions is [-4, 1, 8]. Apply the stated odd/even convention to obtain 1/1; the even-length median need not be an observed value.

3/2

The sorted list retaining repetitions is [-2, -2, 5, 5]. Apply the stated odd/even convention to obtain 3/2; the even-length median need not be an observed value.

2/1

The sorted list retaining repetitions is [-7, -7, 2, 8, 8]. Apply the stated odd/even convention to obtain 2/1; the even-length median need not be an observed value.

-3/1

The sorted list retaining repetitions is [-7, -7, -7, 1, 8, 8]. Apply the stated odd/even convention to obtain -3/1; the even-length median need not be an observed value.

4/1

The sorted list retaining repetitions is [-8, -1, -1, 9, 9, 9]. Apply the stated odd/even convention to obtain 4/1; the even-length median need not be an observed value.

0/1

The sorted list retaining repetitions is [-9, -9, 0, 0, 0, 10]. Apply the stated odd/even convention to obtain 0/1; the even-length median need not be an observed value.

-9/2

The sorted list retaining repetitions is [-10, -10, -10, 1, 11, 11]. Apply the stated odd/even convention to obtain -9/2; the even-length median need not be an observed value.

11/2

The sorted list retaining repetitions is [-11, -1, -1, 12, 12, 12]. Apply the stated odd/even convention to obtain 11/2; the even-length median need not be an observed value.

0/1

The sorted list retaining repetitions is [-12, -12, 0, 0, 0, 13]. Apply the stated odd/even convention to obtain 0/1; the even-length median need not be an observed value.

-6/1

The sorted list retaining repetitions is [-13, -13, -13, 1, 14, 14]. Apply the stated odd/even convention to obtain -6/1; the even-length median need not be an observed value.

7/1

The sorted list retaining repetitions is [-14, -1, -1, 15, 15, 15]. Apply the stated odd/even convention to obtain 7/1; the even-length median need not be an observed value.

0/1

The sorted list retaining repetitions is [-15, -15, 0, 0, 0, 16]. Apply the stated odd/even convention to obtain 0/1; the even-length median need not be an observed value.

-15/2

The sorted list retaining repetitions is [-16, -16, -16, 1, 17, 17]. Apply the stated odd/even convention to obtain -15/2; the even-length median need not be an observed value.

17/2

The sorted list retaining repetitions is [-17, -1, -1, 18, 18, 18]. Apply the stated odd/even convention to obtain 17/2; the even-length median need not be an observed value.

0/1

The sorted list retaining repetitions is [-18, -18, 0, 0, 0, 19]. Apply the stated odd/even convention to obtain 0/1; the even-length median need not be an observed value.

-9/1

The sorted list retaining repetitions is [-19, -19, -19, 1, 20, 20]. Apply the stated odd/even convention to obtain -9/1; the even-length median need not be an observed value.

10/1

The sorted list retaining repetitions is [-20, -1, -1, 21, 21, 21]. Apply the stated odd/even convention to obtain 10/1; the even-length median need not be an observed value.

0/1

The sorted list retaining repetitions is [-21, -21, 0, 0, 0, 22]. Apply the stated odd/even convention to obtain 0/1; the even-length median need not be an observed value.

-21/2

The sorted list retaining repetitions is [-22, -22, -22, 1, 23, 23]. Apply the stated odd/even convention to obtain -21/2; the even-length median need not be an observed value.

23/2

The sorted list retaining repetitions is [-23, -1, -1, 24, 24, 24]. Apply the stated odd/even convention to obtain 23/2; the even-length median need not be an observed value.

0/1

The sorted list retaining repetitions is [-24, -24, 0, 0, 0, 25]. Apply the stated odd/even convention to obtain 0/1; the even-length median need not be an observed value.

-12/1

The sorted list retaining repetitions is [-25, -25, -25, 1, 26, 26]. Apply the stated odd/even convention to obtain -12/1; the even-length median need not be an observed value.

13/1

The sorted list retaining repetitions is [-26, -1, -1, 27, 27, 27]. Apply the stated odd/even convention to obtain 13/1; the even-length median need not be an observed value.

0

Subtract the least observation from the greatest to obtain 0. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

0

Subtract the least observation from the greatest to obtain 0. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

12

Subtract the least observation from the greatest to obtain 12. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

7

Subtract the least observation from the greatest to obtain 7. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

15

Subtract the least observation from the greatest to obtain 15. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

17

Subtract the least observation from the greatest to obtain 17. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

19

Subtract the least observation from the greatest to obtain 19. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

21

Subtract the least observation from the greatest to obtain 21. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

23

Subtract the least observation from the greatest to obtain 23. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

25

Subtract the least observation from the greatest to obtain 25. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

27

Subtract the least observation from the greatest to obtain 27. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

29

Subtract the least observation from the greatest to obtain 29. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

31

Subtract the least observation from the greatest to obtain 31. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

33

Subtract the least observation from the greatest to obtain 33. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

35

Subtract the least observation from the greatest to obtain 35. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

37

Subtract the least observation from the greatest to obtain 37. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

39

Subtract the least observation from the greatest to obtain 39. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

41

Subtract the least observation from the greatest to obtain 41. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

43

Subtract the least observation from the greatest to obtain 43. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

45

Subtract the least observation from the greatest to obtain 45. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

47

Subtract the least observation from the greatest to obtain 47. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

49

Subtract the least observation from the greatest to obtain 49. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

51

Subtract the least observation from the greatest to obtain 51. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

53

Subtract the least observation from the greatest to obtain 53. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

55

Subtract the least observation from the greatest to obtain 55. A singleton or constant list has range zero; this is neither variance nor a count of distinct values.

{0}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {0}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{-3}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-3}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{-4, 1, 8}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-4, 1, 8}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{-2, 5}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-2, 5}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{-7, 8}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-7, 8}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{-7}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-7}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{9}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {9}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{0}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {0}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{-10}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-10}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{12}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {12}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{0}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {0}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{-13}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-13}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{15}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {15}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{0}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {0}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{-16}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-16}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{18}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {18}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{0}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {0}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{-19}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-19}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{21}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {21}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{0}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {0}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{-22}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-22}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{24}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {24}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{0}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {0}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{-25}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-25}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.

{27}

Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {27}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode.