﻿ Standard Deviation Worksheet | Problems & Solutions

# Standard Deviation Worksheet

Standard Deviation Worksheet
• Page 1
1.
A fertilizer is tested on 7 mango trees. The yield of each tree is shown below. 252, 280, 263, 275, 255, 275, 276. Find the mean and variance.
 a. Mean = 278; Variance = 108 b. Mean = 268; Variance = 118 c. Mean = 268; Variance = 108 d. Mean = 258; Variance = 118

#### Solution:

Mean x = 1n i=1n xi = 17 [252 + 280 + 263 + 275 + 255 + 275 +276]

= 17 [1876] = 268

Variance σ2 = 1n i=1n (xi - x)2

= 17 [(252 - 268)2 + (280 - 268)2 + (263 - 268)2 + (275 - 268)2 + (255 - 268)2 + (275 - 268)2 + (276 - 268)2]

= 17 [ 256 + 144 + 25 + 49 + 169 + 49 + 64]

= 17 [756] = 108

2.
The number of watches sold per day are: 11, 18, 15, 16, 15. Find the range and mean.
 a. Range = 7, Mean = 15 b. Range = 8, Mean = 14 c. Range = 7, Mean = 18 d. Range = 8, Mean = 15

#### Solution:

Highest number = 18

Lowest number = 11

Range = 18 - 11 = 7
[Range = Highest number - lowest number.]

Mean x = 1n i=1n xi = 15 [11 + 18 + 15 + 16 + 15] = 15

3.
The grades obtained by 6 students in an exam are: 94, 90, 98, 92, 96, 100. Find
the variance of the data.
 a. 3.4 b. 15.8 c. 11.7 d. 8.3

#### Solution:

Mean x = 1n i=1n xi = 16 [94 + 90 + 98 + 92 + 96 + 100]

= 5706 = 95

Variance σ2 = 1n i=1n (xi - x)2

= 16[(94 - 95)2 + (90 - 95)2 + (98 - 95)2 + (92 - 95)2 + (96 - 95)2 + (100 - 95)2 ]

= 16[1 + 25 + 9 + 9 + 1 + 25]

= 706

» 11.7

4.
A box contains slips numbered 1 through 10. A slip is drawn, and is replaced
after noting its number. The numbers so obtained are 6, 7, 10, 2 and 5. Find the varianceof the numbers obtained.
 a. 6 b. 6.8 c. 6.2

#### Solution:

Mean x = 1n i=1n xi = 15 [6 + 7 + 10 + 2 + 5]

= 305 = 6

Variance σ2 = 1n i=1n (xi - x)2

= 15 [(6 - 6)2 + (7 - 6)2 + (10 - 6)2 + (2 - 6)2 + (5 - 6)2]

=15 [0 + 1 + 16 + 16 + 1]

= 345 » 6.8

5.
The Number of books read by 6 students for three months are : 20, 23, 28, 21, 32, 36. Find the range of the data.
 a. 15 b. 6 c. 16 d. 20

#### Solution:

Highest value = 36

Lowest value = 20

Range = 36 - 20 = 16
[Range = highest value - lowest value.]

6.
The scores in an exam of 8 students are : 98, 82, 80, 90, 84, 93, 81, 88. Find the range of the data.
 a. 80 b. 8 c. 98 d. 18

#### Solution:

Highest score = 98

Lowest score = 80

Range = 98 - 80 = 18
[Range = highest score - lowest score.]

7.
The heights in cm of ten students are: 157, 152, 165, 151, 160, 156, 155, 162, 158, 163. Find the range of the data.
 a. 10 b. 13 c. 14 d. 15

#### Solution:

Maximum height = 165

Minimum height = 151

Range = 165 - 151 = 14
[Range = maximum height - minimum height.]

8.
Number of baskets scored by a basket ball player are: 8, 15, 11, 13, 9, 12, 10. Find the range of the data.
 a. 17 b. 7 c. 6 d. 5

#### Solution:

Highest score = 15

lowest score = 8

Range = 15 - 8 = 7
[Range = highest score - lowest score.]

9.
The number of printing mistakes in ten books are observed as 26, 10, 35, 42, 18, 38, 30, 29, 18 and 39. Find the range of the data.
 a. 22 b. 32 c. 24 d. 34

#### Solution:

Highest number of mistakes = 42

Lowest number of mistakes = 10

Range = 42 - 10 = 32
[Range = highest value - lowest value.]

10.
The weights (in kgs) of six students of a class are: 38, 36, 40, 42, 39, 36. Find the variance of the data.
 a. 3.2 b. 4.6 c. 2.1 d. 6.4

#### Solution:

x = 1n i=1n xi = 16[38 + 36 + 40 + 42 + 39 + 36.]

= 16(231) = 38.5

Variance σ2 = 1n i=1n (xi - x)2

= 16 [(38 - 38.5)2 + (36 - 38.5)2 + (40 - 38.5)2 + (42 - 38.5)2 + (39 - 38.5)2 + (36 - 38.5)2]

= 16[0.25 + 6.25 + 2.25 + 12.25 + 0.25 + 6.25]

= 27.56

» 4.6