TUTORIAL ACTIVITY
1. What are the 4 main measures of variability? Define each. State when you will use them. 2. Professor Dublin has just given a biology exam and wants to calculate the 'range' of performance of his students. What must he do? 3. Professor Dublin wants to ensure he is thorough in his review of student performance, so he decides to calculate 'standard deviation' as well. What must Professor Dublin do to figure out this measure of variability? 4. What is variability? 5. What does standard deviation tell you? 6. When should I use the interquartile range? 7. How do you calculate the Interquartile range?
8. What’s the difference between the range and interquartile range? 9. Can the range be a negative number? 10. What’s the difference between standard deviation and variance? 11. What’s the difference between central tendency and variability? 12. What is a normal distribution?
13. The students in a math test scored the following test results.
11,31,21,19,8,54,35,26,23,13,29,17
a. Find the IQR b. Interpret the test results using IQR, Q1, Q2, Q3 c. Are there any outliers?
14. The students in a quiz scored the following results
58, 15, 26, 10,18, 3, 12, 6, 14, 11
a. Find the IQR b. Interpret the test results using IQR, Q1, Q2, Q3 c. Are there any outliers?
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1. The 4 main measures of variability are:
- Range: The difference between the maximum and minimum values in a dataset. It indicates the spread of the data.
- Interquartile Range (IQR): The difference between the third quartile (Q3) and the first quartile (Q1) in a dataset. It represents the range of the middle 50% of the data and is more resistant to outliers than the range.
- Standard Deviation: It measures how much the values in a dataset deviate from the mean. It provides a measure of the overall spread of the data.
- Variance: It is the average of the squared differences from the mean. It gives an idea of how much the values vary from the mean.
2. Professor Dublin can calculate the range of performance of his students by subtracting the lowest score from the highest score in the exam results.
3. To calculate the standard deviation, Professor Dublin needs to follow these steps:
- Calculate the mean of the data set.
- Subtract the mean from each individual data point and square the result.
- Compute the average of the squared differences.
- Take the square root of the average.
4. Variability refers to the extent to which data points in a data set differ or vary from each other. It describes the spread or dispersion of the data.
5. Standard deviation tells you how much the values in a dataset differ from the mean. It gives a measure of the average amount of variability or dispersion in the data.
6. Interquartile range (IQR) is useful when there are outliers present in the data set, as it is more resistant to outliers than the range. It is also used when you want to focus on the spread of the middle 50% of the data.
7. To calculate the interquartile range, follow these steps:
- Arrange the data set in ascending order.
- Calculate the first quartile (Q1), which is the median of the lower half of the data set.
- Calculate the third quartile (Q3), which is the median of the upper half of the data set.
- Subtract Q1 from Q3 to get the IQR.
8. The range is the difference between the highest and lowest values in a data set, while the interquartile range (IQR) is the difference between the third quartile and the first quartile. The range gives the overall spread of the data, while the IQR focuses on the middle 50% of the data and is less affected by outliers.
9. No, the range cannot be a negative number. It represents the absolute difference between the maximum and minimum values.
10. Standard deviation is the square root of the variance. The variance is the average of the squared differences from the mean. Both measures give a sense of the overall spread or dispersion of the data, but standard deviation is expressed in the same units as the original data, while variance is expressed in squared units.
11. Central tendency measures, such as mean, median, and mode, give an idea of the typical or central value in a data set. They provide information about where the data tends to cluster. Variability measures, such as range, IQR, standard deviation, and variance, give information about the spread, dispersion, or variability of the data points in a data set.
12. A normal distribution is a symmetric, bell-shaped probability distribution that is characterized by its mean and standard deviation. In a normal distribution, the mean, median, and mode are all equal and located at the center of the distribution.
13. a. To find the IQR:
- Arrange the data set in ascending order: 8, 11, 13, 17, 19, 21, 23, 26, 29, 31, 35, 54
- Calculate the first quartile (Q1): Q1 = 17
- Calculate the third quartile (Q3): Q3 = 29
- Calculate the IQR: IQR = Q3 - Q1 = 29 - 17 = 12
b. Q1 represents the 25th percentile (25% of the data falls below this value). Q2 represents the median, which is the middle value in the data set. Q3 represents the 75th percentile (75% of the data falls below this value). The IQR represents the range of the middle 50% of the data.
c. There are no outliers in this data set.
14. a. To find the IQR:
- Arrange the data set in ascending order: 3, 6, 10, 11, 12, 14, 15, 18, 26, 58
- Calculate the first quartile (Q1): Q1 = 10
- Calculate the third quartile (Q3): Q3 = 18
- Calculate the IQR: IQR = Q3 - Q1 = 18 - 10 = 8
b. Q1 represents the 25th percentile (25% of the data falls below this value). Q2 represents the median, which is the middle value in the data set. Q3 represents the 75th percentile (75% of the data falls below this value). The IQR represents the range of the middle 50% of the data.
c. There are no outliers in this data set.