Question 1
5
10
10
5
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Solution: let the number of data be n so sum of data = mean \times number of data = 5n now 10 is subtracted to each data so now sum becomes = 5n10n =5n mean = sum of data /no. of data =\frac{5n}{n} = 5 so new mean becomes 5
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Question 2
8
6
12
Solution: Find the mean \frac{(8+9+12+15+16+20+24+30+32+34)}{10} \frac{(200)}{10} 20 Find the distance of each value from that mean Step 3: Find the mean of those distances \frac{(12+11+8+5+4+0+4+10+12+14)}{10} \frac{80}{8} =8
Question 3
9
Solution: Let us assume that the 10th number is x . we know that, \sigma = \left [ \sqrt{\frac{\sum (x_{i}  \mu)^{2}}{N}} \right ] N = Number of terms. Given that, standard deviation = 2 . Mean = 8 . N = 10 . sum of square of 9 numbers = 599. 10th number = x . So, sum of square of all 10 numbers = Sum of square of 9 numbers+10th Number^{2} Putting all values now , we get : 2=\sqrt{\frac{599+x^{2}}}{10}}(8^{2}) Squaring both sides,we get 4={\frac{599+x^{2}}}{10}}(8^{2}) 4+64={\frac{599+x^{2}}}{10}} 68\times 10=599+x^{2} x^{2}=81 x=9
Question 4
67
40
50
53
Solution: Let’s sort the given data  14, 18, 26, 32, 35, 38, 52, 65 mean = 35 median=\frac{32+35}{2}=33.5 Difference = 35  33.5 = 1.5 Value = 1.5 \times8 = 12 6512 = 53
Question 5
24.166
12.56
23.545
21.66
Solution:
Question 6
14
16
20
18
Solution: Mean=\frac{\text{sum of observations}}{\text{number of observations}} x=\frac{5+7+10+14+x+25+32+19}{8} 112+x=8x 7x=112 x=16
Question 7
2.21
1.41
1.66
1.89
Solution: \sigma = \left [ \sqrt{\frac{\sum (x_{i}  \mu)^{2}}{N}} \right ] \mu=\frac{average}{mean} =21336 \sigma=\sqrt{\frac{1}{5}(2^{2}+1^{2}+0^{2}+1^{2}+2^{2})} \sigma=\sqrt{\frac{1}{5}(4+1+1+4)} \sigma=\sqrt{\frac{10}{5} \sigma=\sqrt{2} =1.41
Question 8
68
55
63
54
Solution: For, 29 observations mean is 33 sum=33\times 29=957 and for 30 observations,mean is 34 sum=34\times 30=1020 Difference=1020957 =63(30th number)
Question 9
Solution: The sequence is 15, 10, 17, 13, 25, 17, 11, 18, 14, 19, 12, 20 Mode=17 Range=2510=15 Median=16 mean of these three=\frac{17+15+16}{3} mean of these three=\frac{48}{3} mean of these three=16
Question 10
32
31.21
22.6
53.45
Solution: \sum (f_{i})=37 \sum (f_{i})\times (u_{i})=1155 Mean=\frac{\sum (f_{i})\times (u_{i})}{\sum (f_{i})} Mean=\frac{1155}{37} Mean=31.21
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