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InterviewSolution
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The following table shows the ages of the patients admitted in a hospital during a year:Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency. |
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Answer» Here, Maximum frequency is `23`. So, Modal class will be corresponding class to `23` that is , `35-45`. Now, Mode can be given by formula, `Mode = l+(f_1-f_0)/(2f_1-f_0-f_2)**h` Here, `l =` Lower limit of modal class `= 35` `f_1 = ` Frequency of Modal class `= 23` `f_2 = ` Frequency of Pre Modal class `= 21` `f_3 = ` Frequency of Succeeding Modal class `= 14` `h =` Class interval `= 10` Putting these values in Mode formula, `Mode = 35+(23-21)/(46-21-14)**10 = 35+2/11**10 = 35+1.8=36.8``Mode = 36.8` means maximum number of patients are of age `36.8` years. Now, we will calculate mean for the given data. Here, we can use step deviation method to find the mean of given data. First we have to construct a table for the given data. Please refer to video for creating complete table. We know, Mean,`(barX) = a+(sumf_iu_i)/(sumf_i)**h` Here, `a =` assumed mean `= 30` `sumf_iu_i = 430` `sumf_i = 80` `h =` step size `=1` Putting these values in formula, `barX = 30+(430)**1/80 = 30+43/8 = 30+5.38 = 35.38` `Mean = 35.38` means average age of the patients is `35.38` years. |
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