Question

Here are test scores for a class of 20 students. 0, 45, 55, 60, 75, 75, 75, 80, 80, 80, 85, 85, 85, 85, 85, 85, 90, 90, 95, 100 (a)Determine the mean and median. (b)Remove 2 quiz scores so the median remains the same. (c)Remove 2 quiz scores so the median increases. (d)Remove 2 quiz scores so the mean decreases. (e)Remove 2 quiz scores so the median stays the same and the mean decreases.

Answer 1

The mean of the test scores is 75.25, and the median is 85. To remove two quiz scores while keeping the median the same, you can remove two scores from the middle of the ordered list. To remove two quiz scores and increase the median, remove the lowest and highest scores from the ordered list. To remove two quiz scores and decrease the mean, remove two scores that are above the mean.

Step-by-step explanation:

The mean is the average of the test scores, which is found by summing all the scores and dividing by the total number of scores. In this case, the sum is 1505 and there are 20 scores, so the mean is 1505/20 = 75.25.

The median is the middle value of the test scores when arranged in numerical order. In this case, when the scores are arranged in ascending order, the middle two values are 85 and 85. Therefore, the median is the average of these two values, which is 85.

(b) To remove two quiz scores while keeping the median the same, we need to remove two scores from the middle of the ordered list. For example, we can remove the two 85 scores to get the new list: 0, 45, 55, 60, 75, 75, 75, 80, 80, 80, 90, 90, 95, 100. The median is still 85.

(c) To remove two quiz scores and increase the median, we can remove the lowest and highest scores from the ordered list. For example, we can remove the 0 and 100 scores to get the new list: 45, 55, 60, 75, 75, 75, 80, 80, 80, 85, 85, 85, 85, 85, 90, 90, 95. The median is now 85.

(d) To remove two quiz scores and decrease the mean, we need to remove two scores that are above the mean. For example, we can remove the 100 and 95 scores to get the new list: 0, 45, 55, 60, 75, 75, 75, 80, 80, 80, 85, 85, 85, 85, 85, 90, 90. The mean is now 1470/18 = 81.67.

(e) To remove two quiz scores while keeping the median the same and decreasing the mean, we can remove one score below the mean and one score above the mean. For example, we can remove the 0 and 100 scores to get the new list: 45, 55, 60, 75, 75, 75, 80, 80, 80, 85, 85, 85, 85, 85, 90, 90, 95. The median is still 85 and the mean is now 1470/18 = 81.67.

Answer 2

a. 1. Mean: 75.5, 2. Median: 82.5

b. The correct option is 4.

c. The correct option is 2.

d. The correct option is 5.

e. The correct option is 3.

Given the scores:

`\[ 0, 45, 55, 60, 75, 75, 75, 80, 80, 80, 85, 85, 85, 85, 85, 85, 90, 90, 95, 100 \]`

(a) Determine the mean and median:

Mean:

Median:

Arranging the scores in ascending order:

`\[ 0, 45, 55, 60, 75, 75, 75, 80, 80, 80, 85, 85, 85, 85, 85, 85, 90, 90, 95, 100 \]`

The median is the average of the 10th and 11th scores:

`\[ \text{Median} = (80 + 85)/(2) = 82.5 \]`

Now, let's address the other parts of the question:

(b) Remove 2 quiz scores so the median remains the same:

To keep the same median, we should remove two scores around the median. Removing the 10th and 11th scores (both 80 and 85), the median remains unchanged at 82.5.

(c) Remove 2 quiz scores so the median increases:

To increase the median, we should remove scores below the current median and above it. If we remove the 1st and 2nd scores (0 and 45), the new median becomes the average of the 9th and 10th scores: 82.5.

(d) Remove 2 quiz scores so the mean decreases:

To decrease the mean, we should remove higher values. If we remove the highest two scores (95 and 100), the new mean becomes:

`\[ \text{New Mean} = (0 + 45 + 55 + \dots + 90)/(18) = (1410)/(18) = 78.33 \]`

(e) Remove 2 quiz scores so the median stays the same and the mean decreases:

To achieve this, we need to remove scores around the higher end. If we remove the 19th and 20th scores (both 95 and 100), the new mean becomes:

`\[ \text{New Mean} = (0 + 45 + 55 + \dots + 90)/(18) = (1410)/(18) = 78.33 \]`

The complete question is here:

Here are test scores for a class of 20 students.

0, 45, 55, 60, 75, 75, 75, 80, 80, 80, 85, 85, 85, 85, 85, 85, 90, 90, 95, 100

(a) Determine the mean and median.

1. Mean

2. Median

(b) Remove 2 quiz scores so the median remains the same.

1. 85, 100

2. 0, 60

3. 45, 90

4. 80, 85

5. 95, 100

(c) Remove 2 quiz scores so the median increases.

1. 0, 100

2. 0, 45

3. 45, 95

4. 95, 100

5. 85, 90

(d) Remove 2 quiz scores so the mean decreases.

1. 55,60

2. 0,45

3. 45,55

4. 45,85

5. 95,100

(e) Remove 2 quiz scores so the median stays the same and the mean decreases.

1. 55,60

2. 0,45

3. 95,100

4. 45,85

5. 60,100