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2. Use the data on Statistics grades to solve for the following:
Grades of
Students arranged in an array
50
57
63
69
72
74
77
80
82
84 87
50
59
65
69
72
75
77
80
82
84
87
50
59
66
69
72
75
77
80
82
85
88
50
60
66
69
72
75
77
81
83
85 89
50
60
68
70
73
75
78
81
83
86 89
50
60
68
71
73
75
79
81
84
86 91
51
62
68
71
73
76
79
81
84
87
92
52
62
68
71
73
76
79
82
84
87
94
53
62
68
71
74
76
79
82
84
87
94
53
62
69
72
74
76
79
82
84
87
96
a) P25
b) D5
c) D₁
d) Q3
e) Range
f) Mean, Median and Mode
​

Sagot :

AlthaeaOfficinalisidn

Answer & Step-by-step explanation:

a) P25

- The data is already arranged in ascending order.

- (total number of grades) = 110

- Position of P25 = 25/100 x (110 + 1)

- Position of P25 = 0.25 × 111 = 27.75

- Position of P25=0.25×111=27.75

Since the position is not an integer, take the average of the 27th and 28th values in the ordered list:

- 27th value: 69

- 28th value: 72

25 = 69+72/2 = 141/2 = 70.5

So, 25 ≈ 70.5

b) D5 (5th Decile)

- Position of D5 = 5/10 × (110 + 1)

- Position of D5 = 0.5 × 111 = 55.5

Take the average of the 55th and 56th values in the ordered list:

- 55th value: 77

- 56th value: 78

5 = 77+78/2 = 155/2 = 77.5

So, 5 ≈ 77.5

c) D₁ (10th Decile)

- Position of D₁ = 10/10 x (110 + 1)

- Position of D₁= 1 x 111 = 111

The 111th value in the ordered list is 96.

₁ = 96

d) Q3 (Third Quartile)

- Position of Q3 = 3/4 x (110 + 1)

- Position of Q3=0.75×111=83.25

Take the average of the 83rd and 84th values in the ordered list:

- 83rd value: 84

- 84th value: 84

Q3 = 84+84/2 = 84

​So, 3 = 84

e) Range

Range = Maximum value − Minimum value

Range = 96 − 50 = 46

So, the range is 46

f) Mean, Median, and Mode

- Mean: Calculate the mean by summing all values and dividing by the number of values (110 in this case).

Mean = ∑values/110

- Median: Since there are 110 values, the median is the average of the 55th and 56th values in the ordered list.

- Mode: Identify the value that appears most frequently in the data set.

The calculations for mean, median, and mode would typically be calculated using software tools for accuracy and efficiency becuase of the large amount of data