Question

In: Statistics and Probability

We surveyed 10 people all in their 20s, asking them the number of books they have...

We surveyed 10 people all in their 20s, asking them the number of books they have read this year.

Age (x) Number of Books Read This Year (y)
20 5
21 2
22 1
23 6
24 0
25 10
26 8
27 1
28 2
29 1

a). Calculate the mean, median, and standard deviation

b). Estimate a regression equation for the two variables

Solutions

Expert Solution

a )

x
(1)		 Frequency (f)
(2)		 f⋅x
(3)=(2)×(1)		 f⋅x2=(f⋅x)×(x)
(4)=(3)×(1)		 cf
(5)
20 5 100 2000 5  
21 2 42 882 7
22 1 22 484 8
23 6 138 3174 14  
24 0 0 0 14
25 10 250 6250 24  
26 8 208 5408   32  
27 1 27 729   33  
28 2 56 1568   35  
29 1 29 841 36  
--- --- --- --- ---
n=36 ∑f⋅x=872 ∑f⋅x2=21336 --

Mean ˉx=∑fx/n

=872/36

=24.2222

Median :
M = value of (n/2)th observation

= value of (36/2)th observation

= value of 18th observation

From the column of cumulative frequency cf, we find that the 18th observation is 25.

Hence, the median of the data is 25.

Standard deviation =  

=

=

= 2.4394

b ) Sum of X = 245
Sum of Y = 36
Mean X = 24.5
Mean Y = 3.6
Sum of squares (SSX) = 82.5
Sum of products (SP) = -10

Regression Equation = ŷ = bX + a

b = SP/SSX = -10/82.5 = -0.12121

a = MY - bMX = 3.6 - (-0.12*24.5) = 6.5697

ŷ = -0.12121X + 6.5697

orchestra answered 2 years ago
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