Answer the following problem. Write your answer to the space provided.
Show your solution and highlight your answer with red color
1. The following data represent the number of books issued in a school library
on selected from 7 different days 7, 9, 12, 15, 5, 4, 11 find the mean number
of books.
2.
A proof reads through 73 pages’ manuscript The number of mistakes found
on each of the pages are summarized in the table below Determine the mean
number of mistakes found per page
3.
Consider the following scores in an activity in statistics;
75.5, 97, 95.5, 100, 93.3, 66.7, 92, 75.5, 73.3, 85.6
What will be the median of all the activities
4.
Find the mode of the given data set: 3, 3, 6, 9, 15, 15, 15, 27, 27, 37, 48
5.
Find the sample variance and standard deviation of the average
temperatures recorded over a five-day period last winter: 18, 22, 19, 25, 12
6.
You and your friends have just measured the heights of your dogs (in
millimeters):
The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm
and 300mm.
Find out the Variance, and the Standard Deviation.
7.
The following data represents the survey regarding the heights (in cm) of 51
girls of Class x. Find the median height.
8.
The following data relates to the daily income of families in an urban area.
Find the modal income of the families.
WRITE YOUR ANSWER TO THE PROVIDED SPACE BELOW
A.
1.
Given: 7, 9, 12, 15, 5, 4, 11
x̄ = ∑f/n
= 7 + 9 + 12 + 15 + 5 + 4 + 11
= 63/7
x̄ = 9
2.
(x)
No. of mistakes
1
2
3
4
5
6
7
Total
x̄ = ∑fiXi / n
= 299 / 73
x̄ = 4.0958 or 4.096
(f)
No. of participants
5
9
12
17
14
10
6
73
Fx
5
18
36
68
70
60
42
299
3. Given: 66.7, 73, 75.5, 75.5, 85.6, 92, 93.3, 95.5, 97, 100
Mdn = ((n/2)th term + ((n/2) + 1)th term/ 2
= 85.6 + 92 /2
Mdn = 88.8
4. Given: 3, 3, 6, 15, 15, 15, 27, 27, 37, 48
Mod= 15
5. Given: 18, 22, 19, 25, 12
Step 1.
x̄ = ∑f/n
= 18 + 22 + 19 + 25 + 12 / 5
= 96/5
= 19.2
Step 2.
X
X - x̄
(X - x̄)2
18
-1.2
1.44
22
2.8
7.84
19
-0.2
0.04
25
5.8
33.64
12
-7.2
51.84
∑ (X - x̄)2 = 94.8
Sample Variance
S = √94.8/ (n-1)
S = √94.8/ (5-1)
= √94.8/4
S = 23.7
Standard Deviation
SD = √variance
SD = √23.7
SD= 4. 868 or 4.87
6.
Step 1.
x̄ = ∑f/n
= 600 + 470 + 170 + 430 + 300 / 5
= 1970 / 5
= 394
Step 2.
X
600
470
170
430
300
(X- x̄)2
42436
5776
50176
1296
8836
X- x̄
206
76
-224
36
-94
∑ (X- x̄)2 = 108520
Sample Variance
S = √ 108520 / (n-1)
S = √ 108520 / (5-1)
S = √ 108520 / 4
S= 27130
Standard Deviation
SD = √variance
SD = √27130
SD= 164.711
7.
Class Limit
135-139
140-144
145-149
150-154
155-159
160-164
Class Boundaries
134.5-139.5
139.5-144.5
144.5-149.5
149.5-154.5
154.5-159.5
159.5-165.5
f
4
7
18
11
6
5
N=51
x
137
142
147
152
157
162
cf
4
11
29
40
46
51
f
5
7
12
18
16
x
50
150
250
350
450
cf
5
12
24
42
58
n/2 = 25.5
Lb = 149.5
cf = 29
fm = 11
cw= 5
x̄ = Lb + (n/2 – cf / fm) cw
x̄ = 149.5 + (25.5 – 29 / 11) 5
x̄ = 147.909 or 147.91
8.
Class Limit
0-100
100-200
200-300
300-400
400-500
Class Boundaries
-0.5-100.5
99.5-200.5
199.5-300.5
299.5-400.5
399.5-500.5
500-600
600-700
499.5-600.5
599.5-700.5
Mode= l + (fm-f1 / 2fm-f1-f2) cw
= 300 + (18-12 / 2(18)-12-16) 100
= 300 + (6 / 36-28) 100
= 300 + (6/8) 100
Mode= 375
10
5
550
650
68
73