Question

A​ walk-in clinic for emergency room services maintains

records of the number of patients it treats per day. The following table shows the frequency of the patient arrivals

over the course of a

168168​-day

period.

a.	Calculate the approximate average number of patients per day.
b.	Calculate the approximate variance and standard deviation of the number of patients per day.

Number of Patients per Day

Frequency

20 to under 40

1717

40 to under 60

2020

60 to under 80

3030

80 to under 100

6161

100 to under 120

4040

a. Calculate the approximate average number of patients per day.

x =

​(Round to one decimal place as​ needed.)

Answer 1

a)

mid-point	frequency
x	f	f*M	f*M2
30	17	510	15300
50	20	1000	50000
70	30	2100	147000
90	61	5490	494100
110	40	4400	484000
total	168	13500	1190400
mean =x̅=Σf*M/Σf=	80.3571
sample Var s2=(ΣfM2-ΣfM2/n)/(n-1)=			632.2070
Std deviation s=		√s2 =	25.1437

a)

approximate average number of patients per day =80.4

b)

approximate variance =632.207 (please take care of number of decimals as required in question and try 628.444 if this comes wrong)

approximate standard deviation =25.144 (please take care of number of decimals as required in question and try 25.069 if this comes wrong)