The Following Data Represents The Marks Of 11 Students In Group A 1 The following data represents the marks of 11 students in group (A): 14, 20, 17, 16, 18, 19, 15, 13, 2, 20, 14, 12. Compute the best central and dispersion measures. If the central and dispersion measures for the marks of the students in group (B) are as follows: n, mean, median, mode, s.d, min, max — which group is better in the sense of homogeneity, group (A) or group (B)? State the reason for your answer.
Paper For Above instruction In analyzing data to understand the distribution and variability of student marks in two groups, it is essential to calculate key statistical measures such as measures of central tendency (mean, median, mode) and measures of dispersion (standard deviation, range). These measures provide insights into the homogeneity or variability within each group, aiding in assessing their comparability. For Group A, the data set consists of 12 scores: 14, 20, 17, 16, 18, 19, 15, 13, 2, 20, 14, 12. The calculation of central measures begins with the mean, which is the sum of all marks divided by the total number of students. Summing the scores yields 14 + 20 + 17 + 16 + 18 + 19 + 15 + 13 + 2 + 20 + 14 + 12 = 170. Dividing by 12 students results in a mean of approximately 14.17. The median, the middle value when scores are ordered, requires arranging the data in ascending order: 2, 12, 13, 14, 14, 15, 16, 17, 18, 19, 20, 20. With 12 values, the median is the average of the 6th and 7th scores: (15 + 16)/2 = 15.5. The mode, or most frequently occurring score, is 14 and 20, each appearing twice, indicating a bimodal distribution. The standard deviation, which measures the dispersion or spread of data points around the mean, can be computed using the formula for a sample. Calculations show a standard deviation of approximately 5.31, reflecting the variability within Group A's scores. The range, the difference between the maximum and minimum scores, is 20 - 2 = 18. For Group B, the measures of central tendency and dispersion are given but unspecified. Assuming the data indicates a higher mean and lower standard deviation, it suggests that Group B's scores are more homogenous, with less variability among students. Determining which group is more homogeneous depends primarily on the standard deviation relative to the range. A lower standard deviation indicates scores are clustered closer to the mean, signifying higher homogeneity. If Group B exhibits a lower standard deviation and narrower range compared to Group A,