The following table shows the ages of the patients admitted in a hospital during a year:
Age (in years) 5-15 15-25 25-35 35-45 45-55 55-65
Number of patients 6 11 21 23 14 5
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.
Answers
Answer:
Step-by-step explanation:
Mode = l + (f1-f0/2f1-f0-f2) ×h
where l is the lower limit of modal class, h is the size of class intervals, f0 is frequency of class preceding the modal class, f1 is the frequency of the modal class and f2 is the frequency of the class succeed in modal class.
Maximum frequency = 23,
Class corresponding to frequency is 35 – 45.
Thus, the modal class is 35 - 45 .
Therefore,l = 35 , h = 45 – 35 = 10, f0 = 21, f1 = 23, f2 = 14
Mode -
= 35 + [(23 - 21)/(2×23- 21 – 14) ]×10
= 35 +[(2 × 10)/(46 - 35)]
= 35 + [20/11]
= 36.81
Thus, the mode age of a patient is 36.81 years
Mean - From the table we will get Σf = 80 and Σfx = 2830
Mean = Σfx /Σf
Mean = 2830/80
= 283/8
= 35.37
Thus, the mean ages of a patient is 35.37 years.
Answer:
Step-by-step explanation:
Mode = l + (f1-f0/2f1-f0-f2) ×h
where l is the lower limit of modal class, h is the size of class intervals, f0 is frequency of class preceding the modal class, f1 is the frequency of the modal class and f2 is the frequency of the class succeed in modal class.
Maximum frequency = 23,
Class corresponding to frequency is 35 – 45.
Thus, the modal class is 35 - 45 .
Therefore,l = 35 , h = 45 – 35 = 10, f0 = 21, f1 = 23, f2 = 14
Mode -
= 35 + [(23 - 21)/(2×23- 21 – 14) ]×10
= 35 +[(2 × 10)/(46 - 35)]
= 35 + [20/11]
= 36.81
Thus, the mode age of a patient is 36.81 years
Mean - From the table we will get Σf = 80 and Σfx = 2830
Mean = Σfx /Σf
Mean = 2830/80
= 283/8
= 35.37
Thus, the mean ages of a patient is 35.37 years.