# The Data on the Number of Patients Attending a Hospital in a Month Are Given Below. Find the Average (Mean) Number of Patients Attending the Hospital in a Month by Using the Shortcut Method. - Mathematics

Sum

The data on the number of patients attending a hospital in a month are given below. Find the average (mean) number of patients attending the hospital in a month by using the shortcut method.  Take the assumed mean as 45. Give your answer correct to 2 decimal places.

 Number of patients 10 -  20 20 - 30 30 - 40 40 - 50 50 - 60 60 -  70 Number of Days 5 2 7 9 2 5

#### Solution

 Number of patients Number of Days (fi) Mid-value xi Assumed Mean A= 45 ∴ d= xi -A fi × di 10  - 20 5 15 -30 -150 20  - 30 2 25 -20 -40 30  - 40 7 35 -10 -70 40 -  50 9 45 0 0 50 -  60 2 55 10 20 60 -  70 5 65 20 100 Total 30 -140

Mean = A + (sumf_i d_i)/(sum f_i)

 = 45+ ((-140))/30 = 45 - 14/3

= (135-14)/3            = 121/3

 = 40.33

Is there an error in this question or solution?