University:
University of Michigan
Course:
MATH 116 | Calculus II
Academic year:

2024
Views:

172

Pages:

2
Author:

banenetta0l

Question 1 Identify the two most commonly used measures of center for quantitative data. Explain the relative advantages and disadvantages of each. Answer Step 1: Advantages and disadvantages of mean: Mean is an important measure of center when the data is quantitative. The mean of a data set is the sum of the data set divided by the size. Step 2: It is a good measure, as it contains all the data and represents the exact center of the data. But it will get highly influenced by outliers in the data set. So, the mean is not a good measure if the data contains outliers. When data is qualitative, one cannot add and divide those data values. So, the mean is not an appropriate measure of center when the data set is qualitative. Advantages and disadvantages of median: The median of a data set is the middle value of the data when the data is arranged in ascending order. Since the median considers only the position, not the data values, it won’t be influenced by the outliers. So, the median is the appropriate measure of central tendency when outliers are present. When the data is qualitative, it is not possible to define an order for that data set. So, the median is not an appropriate measure when the data set is qualitative. Question 2 Use the summation formulas to rewrite the expression without the summation notation. Use the result to find the sums for 𝑛 = 10 , 100 , 1000 , n=10,100,1000, and 10 , 000. ∑ 𝑖 = 1 𝑛 2 𝑖 + 1 𝑛 2 10,000. ∑ i=1 n n 2 2i+1 . Answer: Image Solution Provided. Result: For 𝑛 = 10 → 1.1 n=10→1.1, For 𝑛 = 100 → 1.01 n=100→1.01, For 𝑛 = 1000 → 1.001 n=1000→1.001, For 𝑛 = 10 , 000 → 1.0001 n=10,000→1.0001. Question 3 What is the mode of { 2 , 5 , 6 , 3 , 2 , 8 , 9 , 10 , 2 , 3 , 1 , 17 , 20 , 2 } {2,5,6,3,2,8,9,10,2,3,1,17,20,2}? Answer: Explanation: The mode is the number that occurs most often in a sequence, and since there are 4 copies of the number 2, and only 1 or 2 of all the other numbers, then the number that appears most often is the number 2. Answer: 2 Question 4 What is the median for the following data set: 10 , 8 , 16 , 2 10,8,16,2? Answer: It's 9 - the mean between 8 and 10. Median is defined as the middle value, once the data set is ordered according to value. So in your case this would give 2 , 8 , 10 , 16 2,8,10,16. If there are two middle values, the median is defined as the mean between them. With larger data sets this usually doesn’t matter much, as the middle values tend to be close. E.g. the heights of say 1000 adult males, or the income of the people of a city. In a data set as small as yours, I would hesitate to give any center or spread measures.