**Title: Comparing Measures of Central Tendency****a) Which measures of central tendency do not exist for this data set? Choose all that apply.**Options:- Mean- Median- Mode- None of these measures**b) Suppose that the measurement 15 (the smallest measurement in the data set) were replaced by 3. Which measures of central tendency would be affected by the change? Choose all that apply.**Options:- Mean- Median- Mode- None of these measures**c) Suppose that, starting with the original data set, the largest measurement were removed. Which measures of central tendency would be changed from those of the original data set? Choose all that apply.**Options:- Mean- Median- Mode- None of these measures**d) The relative values of the mean and median for the original data set are typical of data that have a significant skew to the right. What are the relative values of the mean and median for the original data set? Choose only one.**Options:- Mean is greater- Median is greater- Cannot be determined**Additional Instruction:**- Press "Check" to verify your answers.- Use the "Explanation" for detailed information on each question. **Title: Understanding Headache Pain Ratings Using Statistics**In this educational module, we explore the application of statistical measures—mean, median, and mode—to understand personal experiences of headache pain. A study was conducted by a drug manufacturer to assess headache severity on a scale from 0 to 100, where 0 indicates no pain and 100 indicates extreme pain.**Data Collected:**The headache ratings collected are as follows:15, 16, 17, 17, 17, 29, 29, 31, 33, 38, 44, 47, 55, 63, 78, 85, 88**Graphical Representation:**The graph displayed is a frequency distribution of the headache ratings. The x-axis represents the headache rating scale from 0 to 100, while the y-axis indicates the frequency of each rating:- Ratings 0-50 show a slight increase in frequency, with a noticeable peak around the rating of 17.- Frequency decreases again after the rating of 47.- The graph suggests that most data points are concentrated between ratings 15 to 47.**Statistical Measures:**- **Mean:** The average of all headache ratings.- **Median:** The middle value when all ratings are arranged in order.- **Mode:** The most frequently occurring rating.**Questions for Consideration:**(a) Which measures of central tendency (mean, median, mode) are appropriate for this dataset? Select all that apply.This analysis will help in better understanding statistical concepts and how they can be used to interpret real-world data, such as patient experiences with headache severity.

Mean: Mean is defined as the ratio of sum of all observations to the total number of all observations and it is given by Mean =∑xi/n [ where ∑xi is sum of all observations and n = total number of all observations] Median: Median is exactly middle value of the data. If the data set is odd numbered, then Median is exactly the middle value when data is in ascending Order. If the data set is even numbered, then Median is the average of the two middle values when data is in ascending Order. Mode: Mode is the mostly repeated observation in the data set. a) None of these measures is correct. Because Mean, median & Mode can be determine by using given data Given data is, 15, 16, 17, 17, 17, 27, 29, 29, 31, 33, 38, 44, 47, 55, 63, 78, 85, 88 Thus, the mean is 40.5 Median : Data set is even i.e., n = 18 So, median = (31+33)/2 = 32 Thus, median is 32 Mode : 15, 16, 17, 17, 17, 27, 29, 29, 31, 33, 38, 44, 47, 55, 63, 78, 85, 88 Most repeated value in data set is 17 Thus, mode is 17 Hence, the answer is (d) None of these measures b) Mean will change. Since, mean is mostly affected by the extreme value Lets check, New data set is 3, 16, 17, 17, 17, 27, 29, 29, 31, 33, 38, 44, 47, 55, 63, 78, 85, 88 Then mean will be , Median remains same. Because, median is least affected by the outlier value. New data set is 3, 16, 17, 17, 17, 27, 29, 29, 31, 33, 38, 44, 47, 55, 63, 78, 85, 88 So, median = (31+33)/2 = 32 Thus, median is 32 Mode also remains same. Because, mode is least affected by the outlier value. Till, Most repeated value in data set is 17 Thus, mode is 17 Hence, Answer is (a) Mean Largest measure removed from data then data is, 15, 16, 17, 17, 17, 27, 29, 29, 31, 33, 38, 44, 47, 55, 63, 78, 85 Find mean , Hence, mean changed Median - 15, 16, 17, 17, 17, 27, 29, 29, 31, 33, 38, 44, 47, 55, 63, 78, 85 Now, Data set is odd i.e., n = 17 So, median is middle value 31 Thus, median is 32 Hence, median changed Mode will remains same. Because, till most repeated value in data set is 17 Hence (a) Mean & b) Median is correct. Question (d) : For right skewed data. Mean is always greater than median & mode Hence, answer is (a) Mean is greater