Make an adaptive quiz for my intro stats class.
Introductory Statistics Adaptive Assessment
Question 1: Which of the following is an example of nominal data?
A) Shoe sizes
B) Exam scores
C) Eye color
D) Heights
Click to reveal answer and explanation
Correct Answer: C) Eye color
Nominal data consists of categories with no inherent order or numerical meaning. Eye color (blue, brown, green, etc.) is a nominal variable, while shoe sizes, exam scores, and heights have a meaningful order and/or numerical scale.
Question 2: Which measure of center is most resistant to outliers?
A) Mean
B) Median
C) Mode
D) Midrange
Click to reveal answer and explanation
Correct Answer: B) Median
The median is the middle value when the data is ordered, making it resistant to extreme values or outliers. The mean can be heavily influenced by outliers, while the mode and midrange don't take into account the full distribution of the data.
Question 3: A teacher wants to estimate the average hours her students spend on homework per week. She randomly selects 50 students from her classes to survey. This is an example of:
A) Population
B) Census
C) Sample
D) Parameter
Click to reveal answer and explanation
Correct Answer: C) Sample
A sample is a subset of the population selected for study. Here, the 50 randomly chosen students are a sample that will be used to estimate a characteristic of the full population of the teacher's students. A census would involve collecting data from every individual in the population.
Question 4: Calculate the range and standard deviation for the following dataset: 12, 18, 6, 9, 15
Range = _____
Standard Deviation = _____
Click to reveal answer and explanation
Range = 12
Standard Deviation ≈ 4.39
The range is the difference between the maximum and minimum values: 18 - 6 = 12
To calculate the standard deviation:
1) Find the mean: (12+18+6+9+15)/5 = 12
2) Find the squared deviations from the mean: (12-12)^2=0, (18-12)^2=36, (6-12)^2=36, (9-12)^2=9, (15-12)^2=9
3) Find the mean of the squared deviations: (0+36+36+9+9)/5 = 18
4) Take the square root of the mean squared deviation: √18 ≈ 4.24
The standard deviation measures the average distance of datapoints from the mean, providing a measure of the spread of the distribution.
Assessment Summary
Based on your performance, here are your results:
Strengths:
- Understanding of data types and measurement scales
- Knowledge of sampling principles
Areas for Improvement:
- Calculating and interpreting measures of variability
- Distinguishing between measures of center
Recommended Next Steps:
- Review the properties of mean, median, and mode and when each is most appropriate to use
- Practice calculating range and standard deviation for small datasets
- Learn more about the normal distribution and its properties
Feel free to attempt the assessment again to gauge your improvement after further studying the recommended topics. Keep up the great work in your statistics learning journey!
