Question

1. - / 2 points an instructor has graded 27 exam papers submitted by students in a class of 28 students, and the average so far is 65. how high would the score on the last paper have to be to raise the class average by 1 point? by 2 points? 6. - / 4 points consider a sample with data values of 27, 24, 21, 16, 30, 35, 28, and 24. compute the 20th, 25th, 65th, and 75th percentiles. 20th percentile 25th percentile 65th percentile 75th percentile

Explanation:

Question 5

Step1: Find total of 27 papers

The average of 27 papers is 65, so total is \( 27 \times 65 \).
\( 27 \times 65 = 1755 \)

Step2: Find desired total for 28 papers (average 66)

Desired average is \( 65 + 1 = 66 \), so total for 28 papers is \( 28 \times 66 \).
\( 28 \times 66 = 1848 \)

Step3: Find score of last paper (raise by 1)

Subtract total of 27 from total of 28: \( 1848 - 1755 = 93 \)

Step4: Find desired total for 28 papers (average 67)

Desired average is \( 65 + 2 = 67 \), so total for 28 papers is \( 28 \times 67 \).
\( 28 \times 67 = 1876 \)

Step5: Find score of last paper (raise by 2)

Subtract total of 27 from total of 28: \( 1876 - 1755 = 121 \)

Step1: Sort the data

Data values: 27, 24, 21, 16, 30, 35, 28, 24
Sorted: 16, 21, 24, 24, 27, 28, 30, 35 (n = 8)

Step2: Formula for percentile \( P \): \( i = \frac{P}{100} \times n \)

20th percentile:

\( i = \frac{20}{100} \times 8 = 1.6 \)
Since \( i \) is not integer, round up to 2. The 2nd value in sorted data is 21.

25th percentile:

\( i = \frac{25}{100} \times 8 = 2 \)
Average of 2nd and 3rd values: \( \frac{21 + 24}{2} = 22.5 \)

65th percentile:

\( i = \frac{65}{100} \times 8 = 5.2 \)
Round up to 6. The 6th value is 28.

75th percentile:

\( i = \frac{75}{100} \times 8 = 6 \)
Average of 6th and 7th values: \( \frac{28 + 30}{2} = 29 \)

Answer:

To raise by 1 point: 93
To raise by 2 points: 121

Question 6