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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
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Solution

Number of patients  Number of Days (fi)

Mid-value

x

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`

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