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Calculating Mean, Median and Mode for TV Watching Data

Added on -2019-09-23

This article explains how to calculate mean, median and mode for TV watching data collected by an individual and their parents. It also discusses the concept of central tendency and includes a box plot for better visualization. The article is relevant for students studying statistics and data analysis.
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Q1.If the data collected by him for ten days for watching television is taken intoconsideration then Mean = sum of all minutes / total no. of days(73 + 80 + 65 + 20 + 69 + 75 + 72 + 73 + 68 + 70)/10665/1066.5Thus mean = 66.5 minutesMedian is calculated by sorting the data in ascending or descending order. Sort the data inascending order we get20 65 68 69 70 72 73 73 75 80 Since the no. of days are even so median is calculated at n/2 and (n+2)/2 positions. So weget n/2 = 10/2 = 5 and (n+2)/ = 12/2 = 6Now mean is calculated at 5th and 6th position data given hence mean = (70 + 72) /2142/271Thus Median = 71 minutesFor calculating mode we know that mode is the value of data that is most frequentlyoccurring. Hence in this given data 73 is the most frequent value that occurs mostly.Thus Mode = 73 minutesNow if the data collected by his parents are considered then the value of mean , medianand mode are as follows:Mean = (70 + 80 + 86 + 72 + 69 + 76 + 78 + 74 + 83 + 85)/10773/1077.3Thus Mean = 77.3 minutes Now for Median sort the data in ascending order as 69 70 72 74 76 78 80 83 85 86n/2 = 5th position which is 76 and (n+2)/2 that is 6th position which is 78Thus median is equal to = (76 +78)/2154/277 minutes Thus Median = 77 minutesAs there is no value in the data given which is most frequent repeating hence there is nomode here.Q2.If we look over the values got form above question then we see that we received themean value as 66.5 minutes for the data collected by him which is much closer to theprobability of 70 minutes but the mean calculated by the data collected by parents is 77.3minutes which is much higher than the expected average value of watching Television.Q3.The variable that has been looked here is the minutes variable as it is an independentvariable which can change while making the experiment. The measure of centraltendency that is most accurately defining this variable of minutes is the value of mean asthere is no outlier in the given data and there are no extreme scores in the distribution.Q4.The Box Plot is drawn for the data collected by him is as below where Mean = 66.5 Median =71 and Mode = 73 Now C is the value of median in box plot as 71 then make two half lists separating thecomplete list taking the median as 71 so we get two lists as 20 65 68 69 70 and 72 73 73 75 80 thus the median of each half list is as 68 and 73respectively hence the Box Plot is plotted as below.In this Box Plot value of five points are as 20 which is A , 68 as B , 71 as C, 73 as D and80 as D.

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