lessons 1-8 to 1-10b
1. consider the following test scores earned by students in mr. hastert’s history class.
45 63 65 70 71 71 74 86
a. calculate the mean.
68.25
b. what is the mode?
71
c. calculate the median (q2).
70.5
d. what is q1?
64
e. what is q3?
72.5
f. find the interquartile range (iqr)
63
g. state the range.
41
h. draw a box-and-whisker plot for the data.
box - and - whisker plot image with number line from 40 to 90
2. suppose there is a poll about the rating of success for early graduates, high school graduates. the rating is a scale from 1 - 10 where 1 is bad and need to go back to school and 10 is all is perfect and living the dream.
10 2 5 6 7 6 2 8 5
2 2 5 5 6 6 7 8 10
a.) what is the mean, median and mode?
6
b.) what range of ratings were in the lower 25 percentile for responses?
c.) what is the probability a person would respond with a 7?
e.) what kind of probability is this? experimental or theoretical?
d.) make an argument using this data collected?

Question

lessons 1-8 to 1-10b
1. consider the following test scores earned by students in mr. hastert’s history class.
45 63 65 70 71 71 74 86
a. calculate the mean.
68.25
b. what is the mode?
71
c. calculate the median (q2).
70.5
d. what is q1?
64
e. what is q3?
72.5
f. find the interquartile range (iqr)
63
g. state the range.
41
h. draw a box-and-whisker plot for the data.
box - and - whisker plot image with number line from 40 to 90
2. suppose there is a poll about the rating of success for early graduates, high school graduates. the rating is a scale from 1 - 10 where 1 is bad and need to go back to school and 10 is all is perfect and living the dream.
10 2 5 6 7 6 2 8 5
2 2 5 5 6 6 7 8 10
 a.) what is the mean, median and mode?
6
 b.) what range of ratings were in the lower 25 percentile for responses?
 c.) what is the probability a person would respond with a 7?
 e.) what kind of probability is this? experimental or theoretical?
 d.) make an argument using this data collected?

Accepted Answer

### Problem 1 (Test Scores: 45, 63, 65, 70, 71, 71, 74, 86)
#### A. Calculate the Mean
# Explanation:
## Step1: Sum all scores
$45 + 63 + 65 + 70 + 71 + 71 + 74 + 86 = 545$
## Step2: Divide by number of scores (8)
$\frac{545}{8} = 68.125$
# Answer: $68.125$

#### B. What is the Mode?
# Brief Explanations: The mode is the most frequent value. 71 appears twice, others once.
# Answer: $71$

#### C. Calculate the Median (Q2)
# Explanation:
## Step1: Order data (already ordered: 45, 63, 65, 70, 71, 71, 74, 86)
## Step2: Middle two values (4th and 5th: 70, 71)
## Step3: Average them: $\frac{70 + 71}{2} = 70.5$
# Answer: $70.5$

#### D. What is Q1?
# Explanation:
## Step1: Lower half: 45, 63, 65, 70 (first 4 values)
## Step2: Median of lower half: $\frac{63 + 65}{2} = 64$
# Answer: $64$

#### E. What is Q3?
# Explanation:
## Step1: Upper half: 71, 71, 74, 86 (last 4 values)
## Step2: Median of upper half: $\frac{71 + 74}{2} = 72.5$
# Answer: $72.5$

#### F. Find the Interquartile Range (IQR)
# Explanation:
## Step1: IQR = Q3 - Q1
## Step2: $72.5 - 64 = 8.5$
# Answer: $8.5$

#### G. State the Range
# Explanation:
## Step1: Range = Max - Min
## Step2: $86 - 45 = 41$
# Answer: $41$

#### H. Draw a Box - and - Whisker Plot
- Minimum: 45
- Q1: 64
- Median (Q2): 70.5
- Q3: 72.5
- Maximum: 86
Plot: Whisker from 45 to 64, box from 64 to 72.5 (line at 70.5), whisker to 86.

### Problem 2 (Poll Ratings: 10, 2, 5, 6, 7, 6, 2, 8, 5)
#### a.) Mean, Median, Mode
- **Mean**:
  # Explanation:
  ## Step1: Sum: $10 + 2 + 5 + 6 + 7 + 6 + 2 + 8 + 5 = 51$
  ## Step2: Divide by 9: $\frac{51}{9} \approx 5.67$
  # Answer: $\approx 5.67$

- **Median**:
  # Explanation:
  ## Step1: Order: 2, 2, 5, 5, 6, 6, 7, 8, 10
  ## Step2: Middle value (5th): 6
  # Answer: $6$

- **Mode**:
  # Brief Explanations: 2, 5, 6 each appear twice (most frequent).
  # Answer: $2, 5, 6$

#### b.) Lower 25th Percentile (Q1) Range
# Explanation:
## Step1: Order data: 2, 2, 5, 5, 6, 6, 7, 8, 10 (9 values)
## Step2: Lower half (first 4 values: 2, 2, 5, 5)
## Step3: Q1 is median of lower half: $\frac{2 + 5}{2} = 3.5$
## Step4: Lower 25%: values ≤ Q1 (2, 2)
# Answer: Ratings ≤ 3.5 (i.e., 2)

#### c.) Probability of Responding with 7
# Explanation:
## Step1: Number of 7s: 1
## Step2: Total responses: 9
## Step3: Probability: $\frac{1}{9} \approx 0.111$
# Answer: $\frac{1}{9} \approx 0.111$

#### e.) Type of Probability (Experimental/Theoretical)
# Brief Explanations: Based on poll data (experiment), so experimental.
# Answer: Experimental

#### d.) Argument Using Data
# Brief Explanations: Most ratings (2,5,6) are moderate (2 - 6), with a few high (7,8,10). Median 6 suggests a central tendency of moderate success, but some view it highly (10,8,7).
# Answer: Most responses (e.g., 2,5,6) indicate moderate success (2 - 6), with a median of 6. However, a few (7,8,10) show higher satisfaction, suggesting mixed perceptions of early graduate success.

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QUESTION IMAGE

Question

Explanation:

Problem 1 (Test Scores: 45, 63, 65, 70, 71, 71, 74, 86)

A. Calculate the Mean

Step1: Sum all scores

Step2: Divide by number of scores (8)

Step1: Order data (already ordered: 45, 63, 65, 70, 71, 71, 74, 86)

Step2: Middle two values (4th and 5th: 70, 71)

Step3: Average them: $\frac{70 + 71}{2} = 70.5$

Answer:

B. What is the Mode?