Answer :
Let's analyze each statement based on Mikasa's score being at the 70th percentile.
A. "She scored above 70% of her classmates." This is true. By definition, being in the 70th percentile means she scored higher than 70% of the test-takers.
B. "Thirty percent of the class got scores of 55 and above." This is also true. Since 70% scored below her, the remaining 30% scored at or above her level.
C. "If the passing mark is the first quartile, she passed the test." The first quartile, or 25th percentile, means she needed to score above the bottom 25% of her class to pass. Since she is at the 70th percentile, she certainly passed.
D. "Her score is below the 5th decile." Deciles divide data into ten equal parts, and the 5th decile is equivalent to the 50th percentile. Since Mikasa's score is the 70th percentile, this statement is NOT true.
The answer is D.
If 75% of the students have weights of less than or equal to 61.45:
A. "The third Quartile of the data is equal to 61.45." This is true because Q3 or the third quartile corresponds to the 75th percentile.
B. "The median of the data is equal to 61.45." This is NOT true. The median is the 50th percentile, not the 75th.
C. "P75 of the data is equal to 61.45." This is true as P75 is the 75th percentile.
D. "The remaining 25% of the data have weights of more than 61.45." This is true because if 75% are less than or equal, then 25% are more.
The statement that is NOT true is B.
Determine Resty's percentile rank:
Arrange the scores in ascending order: Evelyn (28), Joel (30), Emma (31), Roger (35), Tess (36), Adore (38), Resty (40), Marilyn (42), Mike (45), Alberto (48).
Resty is the 7th score out of 10. The percentile rank can be calculated by:
[tex]P = \left( \frac{\text{Position} - 1}{n} \right) \times 100 = \left( \frac{7-1}{10} \right) \times 100 = 60 \%[/tex]
Since 6 scores are below Resty out of 10, Resty's position corresponds to just above the 60th percentile.
So, none of the choices match precisely, but if following typical education system choices, A could align closest depending on error or assumptions in prior setup.
Third Quartile student:
The third quartile position (Q3) is at [tex]\frac{3(n+1)}{4}[/tex]:
[tex]Q3 = \frac{3(10+1)}{4} = 8.25[/tex]
Thus, the 8th student in sorted order is Marilyn.
The answer is A.
Class width calculation:
The class width is the difference between the upper boundary of one class and the lower boundary of the next class. Taking the first class:
[tex]\text{Class width} = 79.5 - 75 = 4.5[/tex]
The answer is B.
Determine P70:
Looking at the cumulative distribution, P70 lies in the "84.0 - 88.4" interval. Using interpolation for precise calculation would find P70 within this range, making B (88.9) the closest appropriate answer based on cumulative logic.
Level of measurement for rankings like academic position:
Nora's rank is an example of Ordinal scale measurement, which represents ordered categories.
The answer is C.
Mr. Rodolfo and class average:
The most commonly used measure for average and class performance is the Mean as it balances out and considers all data points.
The answer is A.
Teacher Josine on popular anime:
The most appropriate measure for determining popularity or the most common data point is the Mode.
The answer is C.
