Question

In: Statistics and Probability

Find the mean for the following frequency tables. (Round your answers to one decimal place.) (a)        ...

Find the mean for the following frequency tables. (Round your answers to one decimal place.)

(a)        
Grade Frequency
49.5–59.5 2
59.5–69.5 3
69.5–79.5 6
79.5–89.5 14
89.5–99.5 5
(b)        
Daily Low Temperature Frequency
49.5–59.5 50
59.5–69.5 30
69.5–79.5 15
79.5–89.5 1
89.5–99.5 0
(c)        
Points per Game Frequency
49.5–59.5 14
59.5–69.5 32
69.5–79.5 15
79.5–89.5 21
89.5–99.5 2

Solutions

Expert Solution

Solution:-

Solution:

a)

Class
(1)
Frequency (f)
(2)
Mid value (x)
(3)
d=x-A/h=x-74.5/10
A=74.5,h=10
(4)
f⋅d
(5)=(2)×(4)
49.5 - 59.5 2 54.5 -2 -4
59.5 - 69.5 3 64.5 -1 -3
69.5 - 79.5 6 74.5=A 0 0
79.5 - 89.5 14 84.5 1 14
89.5 - 99.5 5 94.5 2 10
--- --- --- --- ---
n=30 ----- ----- ∑f⋅d=17

Mean =A+∑fd/n⋅h

=74.5+17/30⋅10

=74.5+0.5667⋅10

=74.5+5.6667

=80.2

b)

Class
(1)
Frequency (f)
(2)
Mid value (x)
(3)
d=x-A/h=x-74.5/10
A=74.5,h=10
(4)
f⋅d
(5)=(2)×(4)
49.5 - 59.5 50 54.5 -2 -100
59.5 - 69.5 30 64.5 -1 -30
69.5 - 79.5 15 74.5=A 0 0
79.5 - 89.5 1 84.5 1 1
89.5 - 99.5 0 94.5 2 0
--- --- --- --- ---
n=96 ----- ----- ∑f⋅d=-129



Mean =A+∑fd/n⋅h

=74.5+-129/96⋅10

=74.5+-1.3438⋅10

=74.5+-13.4375

=61.1

c)

Class
(1)
Frequency (f)
(2)
Mid value (x)
(3)
d=x-A/h=x-74.5/10
A=74.5,h=10
(4)
f⋅d
(5)=(2)×(4)
49.5 - 59.5 14 54.5 -2 -28
59.5 - 69.5 32 64.5 -1 -32
69.5 - 79.5 15 74.5=A 0 0
79.5 - 89.5 21 84.5 1 21
89.5 - 99.5 2 94.5 2 4
--- --- --- --- ---
n=84 ----- ----- ∑f⋅d=-35



Mean =A+∑fd/n⋅h

=74.5+-35/84⋅10

=74.5+-0.4167⋅10

=74.5+-4.1667

=70.3


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