Maths has a median score of \(78\) and a range of \(10\) so all the results were close to the mean and the median. In summary, both English and Maths have a mean score of \(78\) however English has a median score of \(71\) and a range of \(35\) as some students scored much higher than others. This is far greater than the range of scores in the Maths which is \(10\). ![]() The range of scores in English is \(35\). The range is not an average, but a measure of the spread of the values (or marks in this case). However, in order to highlight the differences in the marks scored and to give maximum information, a combination of the median and the range would be best. Range and interquartile range were calculated above so the calculations for calculating mean, variance and standard deviation are provided below for the data presented in Figure 1. The mean is usually the best measure of the average, as it takes into account all of the data values. It depends on the context in which the result is to be used. The modal score for each subject \(96\) and \(78\) suggests that the students did better in English however this is only considering the two top marks in English and you have no information about the scores of the other students. The median is only a measure of the middle value, as there will be the same number of values above and below this middle value. From the image, we can notice the occurrence of the median and. Before determining the interquartile range, we first need to know the values of the first quartile and the third quartile. Its used in statistics to find out how spread-out different values are. This is partly true, but there are also some much higher scores. The interquartile range (IQR) can be defined as the difference between the first quartile and the third quartile. The range is the difference between the largest and smallest number in a set of data. The medians, \(73\) and \(78\) suggest that the students generally scored less well in English. ![]() However, looking at the actual scores, you can see that this is not the case. The first method is to take the data, split it into two equal halves, and then find the middle of the lower half. This suggests that the scores of the students are similar in English and Maths. When we identify limitations on the inputs and outputs of a function, we are determining the domain and range of the function. The lower quartile can be found with two methods. The mean score in each subject is \(78\). If you were to compare the scores in the two subjects, which measure of average would you use and why?
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