The following frequency table summarizes a set of data. what is the five-number summary?

Question1:

Answer1:

For large numbers of data, all methods converge to the same results. For small datasets, the methods differ in how they interpolate gaps in the input data.

Answer2:

Question2

{0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18, 18, 19, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 25, 25, 25, 26, 26, 26, 26, 27, 28, 28, 28, 28, 28, 29, 30, 30, 30, 31, 31, 31, 31, 31, 31, 31, 33, 33, 33, 33, 34, 34, 34, 34, 35, 35, 36, 37, 37, 38, 38, 38, 38, 38, 38, 38, 40, 41, 41, 41, 42, 43, 44, 44, 44, 44, 45, 45, 45, 45, 45, 45, 45, 45, 46, 47, 47, 48, 48, 48, 49, 49, 50, 50, 51, 51, 52, 52, 52, 52, 52, 53, 54, 54, 54, 55, 55, 55, 56, 56, 56, 56, 57, 59, 61, 61, 63, 63, 69, 70, 70, 77, 80}

Answer2

Consider the set:

{1,2,3,4,5,6,7,8,9,10,11,12,13}

Clearly, Q2 is 7, Q1 is 3.5, and Q3 is 10.5. However, your program yields

"Quartile Q1: 4
Quartile Q2: 7
Quartile Q3: 10"

^ This is incorrect.

I think the error in the algorithm is in how it creates the lower and upper halves after finding Q2.

Consider the set:

{1,2,3,4,5,6}

If the list is of even length, Q2 will be the average of the two middle values (e.g. Q2 = [3+4]/2 = 3.5) . Hence, the lower half should be a list ranging from the LOW (i.e. the lowest value in the original set of values) to the floor of Q2 (e.g. if Q2=3.5, the floor of Q2 is 3). Hence,

lower half = {1,2,3}

The upper half should range from the ceiling of Q2 (e.g. is Q2=3.5, the ceiling of Q2 is 4) to the HIGH (i.e. the highest value in the original set of values). Hence,

upper half = {4,5,6)

A visual:

1 2 3 4 5 6
1 * 3 * 4 * 6

Q2 = 3.5
Q1 = 2
Q3 = 5

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The following frequency table summarizes a set of data. What is the five-number summary?

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