example:
science test scores
75, 88, 90, 84, 100, 80, 96, 50, 62, 78, 88
put in order:
50, 62, 75, 78, 80, 84, 88, 88, 90, 96, 100

stem | leaf
5 | 0
6 | 2
7 | 5, 8
8 | 0, 4, 8, 8
9 | 0, 6
10 | 0
key: 5 | 0 means 50.

1. how many students scored below 70?
2. was there a mode(s)? if so, what is it?
3. what is the range of the test scores?
4. is the range less than the mean?
5. if a homework pass is given to anyone who scores 80 or above, how many students will receive the homework pass?
6. if the student who scored 100 actually made a 90, would it change the range?
7. if so, how?
8. also, would it change the mean? would it become higher or lower?

Question

example:
science test scores
75, 88, 90, 84, 100, 80, 96, 50, 62, 78, 88
put in order:
50, 62, 75, 78, 80, 84, 88, 88, 90, 96, 100

stem | leaf
5 | 0
6 | 2
7 | 5, 8
8 | 0, 4, 8, 8
9 | 0, 6
10 | 0
key: 5 | 0 means 50.

1. how many students scored below 70?
2. was there a mode(s)? if so, what is it?
3. what is the range of the test scores?
4. is the range less than the mean?
5. if a homework pass is given to anyone who scores 80 or above, how many students will receive the homework pass?
6. if the student who scored 100 actually made a 90, would it change the range?
7. if so, how?
8. also, would it change the mean? would it become higher or lower?

Accepted Answer

### Question 3: What is the range of the test scores?
# Explanation:
## Step 1: Recall the formula for range
The range of a set of data is calculated as the difference between the maximum value and the minimum value. The formula is $ \text{Range} = \text{Maximum value} - \text{Minimum value} $.

## Step 2: Identify the maximum and minimum values
From the ordered list of scores: $ 50, 62, 75, 78, 80, 84, 88, 88, 90, 96, 100 $, the minimum value is $ 50 $ and the maximum value is $ 100 $.

## Step 3: Calculate the range
Substitute the maximum and minimum values into the range formula: $ \text{Range} = 100 - 50 = 50 $.

# Answer:
$ 50 $

### Question 5: If a homework pass is given to anyone who scores 80 or above, how many students will receive the homework pass?
# Explanation:
## Step 1: Identify scores ≥ 80
From the ordered list $ 50, 62, 75, 78, 80, 84, 88, 88, 90, 96, 100 $, we identify the scores that are 80 or above: $ 80, 84, 88, 88, 90, 96, 100 $.

## Step 2: Count the number of such scores
Count the number of scores in the list from Step 1. There are 7 scores.

# Answer:
$ 7 $

### Question 6: If the student who scored 100 actually made a 90, would it change the range?
# Explanation:
## Step 1: Recall the original range and new values
Original minimum value: $ 50 $, original maximum value: $ 100 $, so original range $ = 100 - 50 = 50 $. After changing 100 to 90, the new maximum value is $ 96 $ (since $ 96 > 90 $) and the minimum value remains $ 50 $.

## Step 2: Calculate the new range
New range $ = 96 - 50 = 46 $. Since the original range was 50 and the new range is 46, the range changes. But the question is just asking if it would change, so we check if the maximum value changes (which it does, from 100 to 96) and since range depends on max and min, and min is same, range will change. Wait, actually, let's re - check: original data points after ordering: 50, 62, 75, 78, 80, 84, 88, 88, 90, 96, 100. If we change 100 to 90, the new ordered list is 50, 62, 75, 78, 80, 84, 88, 88, 90, 90, 96. Now the maximum value is 96, minimum is 50. Original range: 100 - 50 = 50. New range: 96 - 50 = 46. So the range changes. But the question is "would it change the range?" So the answer is yes.

# Answer:
Yes

### Question 7: If so, how?
# Explanation:
## Step 1: Find original and new range
Original range: $ 100 - 50 = 50 $. After changing 100 to 90, the new maximum value is 96 (from the ordered list of new scores: 50, 62, 75, 78, 80, 84, 88, 88, 90, 90, 96). New range: $ 96 - 50 = 46 $.

## Step 2: Determine the change
The range decreases from 50 to 46. So the range would decrease (or the new range is 46, which is less than the original range of 50).

# Answer:
The range would decrease (from 50 to 46)

### Question 8: Also, would it change the mean? Would it become higher or lower?
# Explanation:
## Step 1: Recall the formula for mean
The mean $ \bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n} $, where $ x_{i} $ are the data points and $ n $ is the number of data points.

## Step 2: Analyze the change in sum of scores
Original score sum: $ 50+62 + 75+78+80+84+88+88+90+96+100 $. New score sum: $ 50+62 + 75+78+80+84+88+88+90+96+90 $. The difference between original and new sum: $ 100 - 90=10 $. So the new sum is 10 less than the original sum.

## Step 3: Determine the effect on mean
Since the number of data points $ n $ remains the same (11), and the sum of the scores decreases (by 10), the mean (which is sum divided by $ n $) will decrease. So the mean will change (decrease) because we are replacing a higher score (100) with a lower score (90), which reduces the total sum, and since the number of scores is the same, the mean will be lower.

# Answer:
Yes; Lower

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QUESTION IMAGE

Question

Explanation:

Question 3: What is the range of the test scores?

Step 1: Recall the formula for range

Step 2: Identify the maximum and minimum values

Step 3: Calculate the range

Step 1: Identify scores ≥ 80

Step 2: Count the number of such scores

Step 1: Recall the original range and new values

Step 2: Calculate the new range

Answer:

Question 5: If a homework pass is given to anyone who scores 80 or above, how many students will receive the homework pass?