Question

25	49	66	44	60
36	51	78	41	54
32	54	80	56	48
41	65	64	62	53
47	72	39	69	44

1) Average
2) Medium
3) Q1
4) Q3
5) P63
6) P93
7) Range
8) Variance
9) Standard Deviation
10) Construct a box-mustache graph for the above data.

Answer 1

Number	Values ( X )
1	25
2	32
3	36
4	39
5	41
6	41
7	44
8	44
9	47
10	48
11	49
12	51
13	53
14	54
15	54
16	56
17	60
18	62
19	64
20	65
21	66
22	69
23	72
24	78
25	80

Part 1)

Mean X̅ = Σ Xi / n
X̅ = 1330 / 25 = 53.2

Part 2)

Q2 = (1/2 n + 1/2 )th value
Q2 = (1/2 * 25 + 1/2 )th value
Median (Q2) = 53

Part 3)

Q1 = (1/4 n + 1/4 )th value
Q1 = (1/4 * 25 + 1/4 )th value
Q1 = 42.5

Part 4)

Q3 = (3/4 n + 3/4 )th value
Q3 = (3/4 * 25 + 3/4 )th value
Q3 = 64.5

Part 5)

Percentile = ( P/100 * n + 1/2 )th value
Percentile = ( 63/100 * 25 + 1/2 )th value
Percentile = 57.52

Part 6)

Percentile = ( P/100 * n + 1/2 )th value
Percentile = ( 93/100 * 25 + 1/2 )th value
Percentile = 78.36

Part 7)

Range = Highest value - Lowest value = 55

Lowest value = 25
Highest value = 80

Part 8)

Variance σ2   = ( (Xi - X̅ )2 / n )
σ2  = ( 4786 / 25 ) = 191.44

Part 9)

Standard deviation σ = √( (Xi - X̅ )2 / n ) = 13.8362

Part 10)