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 (SS_X) = 82.5
Sum of products (SP) = -10

Regression Equation = ŷ = bX + a

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

a = M_Y - bM_X = 3.6 - (-0.12*24.5) = 6.5697

ŷ = -0.12121X + 6.5697

orchestra answered 1 year ago

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