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Sagot :
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
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