Question
Question 4 A) Calculate the interquartile range of the following data. Remember that Desmos (right-click and open in new tab/window) can be used to help you calculate some of this. {35, 20, 41, 48, 79, 83, 83, 97, 120}{35, 20, 41, 48, 79, 83, 83, 97, 120}(6 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Q1=Q1=Response area Q3=Q3=Response area IQR = Response area Values lower than Response area and higher than Response area are considered outliers. The outlier in this data set is Response area. -40-1414203852789012014216820 & 120none of these. There are no outliers. Question 5 A)Fill in the blanks to create the formula used to calculate if there are outliers in a given data set. Answers may be used more than once.(4 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Response area−1.5×−1.5×Response area Response area+1.5×+1.5×Response area Q1Q1Q2Q2Q3Q3MeanRangeStandard deviationIQR Question 6 A) Calculate the standard deviation of the data set. Round to the nearest tenth. {20, 35, 41, 48, 79, 83, 83, 97, 120}{20, 35, 41, 48, 79, 83, 83, 97, 120}(1 point) Responses 32.9 32.9 79.0 79.0 29.8 29.8 31.0 31.0 Question 7 A)The ages of the students in a statistics class are listed below. If the 18-year-old student has a birthday and turns 19, how will it affect the mean and median ages of the class? Ages: 14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18(1 point) Responses Both the mean age and the median age will increase. Both the mean age and the median age will increase. The mean age will remain the same, and the median age will decrease. The mean age will remain the same, and the median age will decrease. The mean age will remain the same, and the median age will increase. The mean age will remain the same, and the median age will increase. The mean age will increase, and the median age will remain the same. The mean age will increase, and the median age will remain the same. Question 8 A) Based on the two data sets given below, which of the following statements are true? Select two that apply. Data Set 1: 5, 5, 6, 6, 7, 7 Data Set 2: 1, 3, 5, 7, 9, 11(1 point) Responses Data Set 2 has a larger mean than Data Set 1. Data Set 2 has a larger mean than Data Set 1. Data Set 2 has the same mean as Data Set 1. Data Set 2 has the same mean as Data Set 1. Data Set 2 has a smaller standard deviation than Data Set 1. Data Set 2 has a smaller standard deviation than Data Set 1. Data Set 2 has a larger standard deviation than Data Set 1. Data Set 2 has a larger standard deviation than Data Set 1. Question 9 A)The weight, in pounds, of each cat in an animal shelter is shown in the dot plot below. The kitten that weighs 3 pounds was adopted today and is no longer in the shelter. Which of the following statements is not true about the distribution of the weight of the remaining cats?(1 point) Responses The mean of the weight distribution increased. The mean of the weight distribution increased. The range of the weight distribution decreased. The range of the weight distribution decreased. The standard deviation of the weight distribution decreased. The standard deviation of the weight distribution decreased. The median of the weight distribution increased. The median of the weight distribution increased.
Answers
GPT-4o mini
Let's tackle your questions consecutively.
**Question 4 A: Calculate the interquartile range (IQR)**
Given data: {35, 20, 41, 48, 79, 83, 83, 97, 120}
1. **Organize the data in ascending order**:
{20, 35, 41, 48, 79, 83, 83, 97, 120}
2. **Find Q1 (the first quartile)**:
- The first quartile is the median of the first half of the data (first four numbers): {20, 35, 41, 48}.
- Q1 = (35 + 41) / 2 = 38
3. **Find Q3 (the third quartile)**:
- The third quartile is the median of the second half of the data (last four numbers): {79, 83, 83, 97, 120}.
- Q3 = (83 + 97) / 2 = 90
4. **Calculate the IQR**:
- IQR = Q3 - Q1 = 90 - 38 = 52
**Responses**:
- Q1 = 38
- Q3 = 90
- IQR = 52
**Outliers**:
- The outlier detection boundaries are:
- Lower boundary = Q1 - 1.5 * IQR = 38 - 1.5 * 52 = -25
- Upper boundary = Q3 + 1.5 * IQR = 90 + 1.5 * 52 = 153
- Therefore, any value less than -25 or greater than 153 is considered an outlier.
- Since all data points fall within this range, there are **no outliers**.
**Final Responses** for Question 4:
- Q1 = 38
- Q3 = 90
- IQR = 52
- There are no outliers.
---
**Question 5 A: Fill in the blanks for outlier formula**
The formula to detect outliers based on the IQR is given by:
- Outlier: any value less than \(Q1 - 1.5 \times IQR\) or greater than \(Q3 + 1.5 \times IQR\).
Therefore, fill in:
- Response area = Q1
- Response area = IQR
- Response area = Q3
So the complete formula would be:
- \(Q1 - 1.5 \times IQR\) and \(Q3 + 1.5 \times IQR\).
---
**Question 6 A: Calculate the standard deviation of the data set**
Given data: {20, 35, 41, 48, 79, 83, 83, 97, 120}
1. **Calculate the mean**:
- Mean = (20 + 35 + 41 + 48 + 79 + 83 + 83 + 97 + 120) / 9 = 69.0
2. **Calculate the variance**:
- Deviations: {−49, −34, −28, −21, 10, 14, 14, 28, 51}
- Squared deviations: {2401, 1156, 784, 441, 100, 196, 196, 784, 2601}
- Variance = (sum of squared deviations) / (number of data points) = (2401 + 1156 + 784 + 441 + 100 + 196 + 196 + 784 + 2601) / 9 = 883.44
3. **Calculate the standard deviation**:
- Standard deviation = √Variance = √883.44 ≈ 29.7 (rounded to the nearest tenth).
**Final Response** for Question 6:
- Responses: 29.8 (as the closest option given)
---
**Question 7 A: Effect of the age change on mean and median**
Ages: 14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18
If the 18-year-old turns 19, then:
1. **Mean will increase**:
- The total will be higher (due to the student becoming older).
2. **Median will increase**:
- The middle value changes since the 18 year old is now 19.
**Final Response** for Question 7:
- Both the mean age and the median age will increase.
---
**Question 8 A: Analyze Data Sets**
Data Set 1: {5, 5, 6, 6, 7, 7}
Average = (5+5+6+6+7+7) / 6 = 6
Standard deviation = 0.82 (lower variability)
Data Set 2: {1, 3, 5, 7, 9, 11}
Average = (1+3+5+7+9+11) / 6 = 6
Standard deviation = 4.24 (higher variability)
**True statements**:
1. Data Set 2 has a larger mean than Data Set 1.
2. Data Set 2 has a larger standard deviation than Data Set 1.
**Final Responses** for Question 8:
- Data Set 2 has a larger mean than Data Set 1.
- Data Set 2 has a larger standard deviation than Data Set 1.
---
**Question 9 A: Assessing the impact of removing a cat**
When the 3-pound kitten is adopted:
1. **The mean of the weight distribution will increase** (since the lightest weight is gone).
2. **The range will decrease** (if 3 was the minimum).
3. **If 3 was the minimum**, standard deviation might either increase or decrease depending on the rest of the values.
4. **The median**: Usually, it could increase or decrease depending on the arrangement after the removal.
**Final Response** regarding the statement that is not true:
- The median of the weight distribution increased. (It may not increase, hence this statement is likely false).
---
This is the comprehensive breakdown of all the questions you had. Let me know if anything needs to be clarified further!
**Question 4 A: Calculate the interquartile range (IQR)**
Given data: {35, 20, 41, 48, 79, 83, 83, 97, 120}
1. **Organize the data in ascending order**:
{20, 35, 41, 48, 79, 83, 83, 97, 120}
2. **Find Q1 (the first quartile)**:
- The first quartile is the median of the first half of the data (first four numbers): {20, 35, 41, 48}.
- Q1 = (35 + 41) / 2 = 38
3. **Find Q3 (the third quartile)**:
- The third quartile is the median of the second half of the data (last four numbers): {79, 83, 83, 97, 120}.
- Q3 = (83 + 97) / 2 = 90
4. **Calculate the IQR**:
- IQR = Q3 - Q1 = 90 - 38 = 52
**Responses**:
- Q1 = 38
- Q3 = 90
- IQR = 52
**Outliers**:
- The outlier detection boundaries are:
- Lower boundary = Q1 - 1.5 * IQR = 38 - 1.5 * 52 = -25
- Upper boundary = Q3 + 1.5 * IQR = 90 + 1.5 * 52 = 153
- Therefore, any value less than -25 or greater than 153 is considered an outlier.
- Since all data points fall within this range, there are **no outliers**.
**Final Responses** for Question 4:
- Q1 = 38
- Q3 = 90
- IQR = 52
- There are no outliers.
---
**Question 5 A: Fill in the blanks for outlier formula**
The formula to detect outliers based on the IQR is given by:
- Outlier: any value less than \(Q1 - 1.5 \times IQR\) or greater than \(Q3 + 1.5 \times IQR\).
Therefore, fill in:
- Response area = Q1
- Response area = IQR
- Response area = Q3
So the complete formula would be:
- \(Q1 - 1.5 \times IQR\) and \(Q3 + 1.5 \times IQR\).
---
**Question 6 A: Calculate the standard deviation of the data set**
Given data: {20, 35, 41, 48, 79, 83, 83, 97, 120}
1. **Calculate the mean**:
- Mean = (20 + 35 + 41 + 48 + 79 + 83 + 83 + 97 + 120) / 9 = 69.0
2. **Calculate the variance**:
- Deviations: {−49, −34, −28, −21, 10, 14, 14, 28, 51}
- Squared deviations: {2401, 1156, 784, 441, 100, 196, 196, 784, 2601}
- Variance = (sum of squared deviations) / (number of data points) = (2401 + 1156 + 784 + 441 + 100 + 196 + 196 + 784 + 2601) / 9 = 883.44
3. **Calculate the standard deviation**:
- Standard deviation = √Variance = √883.44 ≈ 29.7 (rounded to the nearest tenth).
**Final Response** for Question 6:
- Responses: 29.8 (as the closest option given)
---
**Question 7 A: Effect of the age change on mean and median**
Ages: 14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18
If the 18-year-old turns 19, then:
1. **Mean will increase**:
- The total will be higher (due to the student becoming older).
2. **Median will increase**:
- The middle value changes since the 18 year old is now 19.
**Final Response** for Question 7:
- Both the mean age and the median age will increase.
---
**Question 8 A: Analyze Data Sets**
Data Set 1: {5, 5, 6, 6, 7, 7}
Average = (5+5+6+6+7+7) / 6 = 6
Standard deviation = 0.82 (lower variability)
Data Set 2: {1, 3, 5, 7, 9, 11}
Average = (1+3+5+7+9+11) / 6 = 6
Standard deviation = 4.24 (higher variability)
**True statements**:
1. Data Set 2 has a larger mean than Data Set 1.
2. Data Set 2 has a larger standard deviation than Data Set 1.
**Final Responses** for Question 8:
- Data Set 2 has a larger mean than Data Set 1.
- Data Set 2 has a larger standard deviation than Data Set 1.
---
**Question 9 A: Assessing the impact of removing a cat**
When the 3-pound kitten is adopted:
1. **The mean of the weight distribution will increase** (since the lightest weight is gone).
2. **The range will decrease** (if 3 was the minimum).
3. **If 3 was the minimum**, standard deviation might either increase or decrease depending on the rest of the values.
4. **The median**: Usually, it could increase or decrease depending on the arrangement after the removal.
**Final Response** regarding the statement that is not true:
- The median of the weight distribution increased. (It may not increase, hence this statement is likely false).
---
This is the comprehensive breakdown of all the questions you had. Let me know if anything needs to be clarified further!