Question

The number of patients treated in a dental office on Mondays was recorded for 11 weeks. 7, 12, 21, 21, 16, 21, 13, 19, 11, 15, 20

a) Complete the chart for this sample set of data?

Mean

Median

Mode

St.Dev

Q 1

Q 2

Q 3

Range

Interquartile Range

Answer 1

Solution:

x	x2
11	121
7	49
12	144
21	441
21	441
16	256
21	441
13	169
19	361
11	121
15	225
20	400
∑x=187	∑x2=3169

Mean ˉx=∑xn

=11+7+12+21+21+16+21+13+19+11+15+20/12

=187/12

=15.5833


Median :
Observations in the ascending order are :
7,11,11,12,13,15,16,19,20,21,21,21

Here, n=12 is even.

M=Value of(n2)thobservation+Value of(n2+1)thobservation2

=Value of(122)thobservation+Value of(122+1)thobservation2

=Value of6thobservation+Value of7thobservation2

=15+162

=15.5


Mode :
In the given data, the observation 21 occurs maximum number of times (3)

∴Z=21Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√3169-(187)212/11

=√3169-2914.0833/11

=√254.9167/11

=√23.1742

=4.814


Arranging Observations in the ascending order, We get :
7,11,11,12,13,15,16,19,20,21,21,21

Here, n=12

Q1=(n+14)th value of the observation

=(134)th value of the observation

=(3.25)th value of the observation

=3rd observation +0.25[4th-3rd]

=11+0.25[12-11]

=11+0.25(1)

=11+0.25

=11.25

Q2=(2(n+1)4)th value of the observation

=(2⋅134)th value of the observation

=(6.5)th value of the observation

=6th observation +0.5[7th-6th]

=15+0.5[16-15]

=15+0.5(1)

=15+0.5

=15.5

Q3=(3(n+1)4)th value of the observation

=(3⋅134)th value of the observation

=(9.75)th value of the observation

=9th observation +0.75[10th-9th]

=20+0.75[21-20]

=20+0.75(1)

=20+0.75

=20.75

Range = Maximum value - Minimum value

= 21 - 7

= 14

Range = 14

Interquartile Range = Q3 - Q1

= 20.75 -11.25

= 9.5

Interquartile Range = 9.5