Math: RANGE, VARIANCE

Compute the following:

A. What is the range of this set: {15, 12, 8, 10, 6, 12, 18}?

● {6, 8, 10, 12, 12, 15, 18}

● 18 - 6 = 12

B. What is the range of this set: {5.2, 3.75, 3.8, 3.8, 8.0, 6.25, 5.2, 8.5}?

● {3.75, 3.8, 3.8, 5.2, 5.2, 6.25, 8.0, 8.5}

● 8.5 - 3.75 = 4.75

C. What is the range of the first 12 consecutive natural numbers?

● {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

● 12 - 1 = 11

D. The ages of the 7 grandchildren of Mrs. Mercado are: 7, 5, 3, 12, 6, 7 and 4 years old.
Compute for the range.

● {3, 4 ,5, 6, 7, 7, 12}

● 12 - 3 = 9

E. Seven students in Statistics class have the following IQ’s: 110, 125, 122, 100, 120, 112
and 127. Determine the range.

● {100, 110, 112, 120, 122, 125, 127}

● 127 - 100 = 27

F. Let x be a natural number. What is the range of this set: {x, x + 1, x - 2, x + 5, x - 3}?

● {x-3, x-2, x, x+1, x+5}

● (x+5) - (x-3) =
● (x+5) + (-x+3)
● 5+3=8

G. Let x be a natural number. What is the range of this set: {x, x + 1, x + 5, x + 4}?

● {x, x+1, x+4, x+5}

● x+5-x=5

This document/presentation contains proprietary and confidential information. Reproduction, redistribution, or forwarding to any third party, in whole or in part, is
This study source wasstrictly prohibited
downloaded unless made with prior
by 100000848672578 fromwritten consent from
CourseHero.com Ayala Education
on 04-11-2023 Inc. Violation
20:36:28 GMT -05:00or noncompliance shall be dealt with according to law.

https://www.coursehero.com/file/158258222/mathematicssscspdf/
 H. What is the variance of this set: {x, x + 1, x + 5, x + 2}?

● MEAN
○ {x, x+1, x+2, x+5}
○ (x + x+1 + x+2 + x+5) / 4
○ 4x + 1 + 2 + 5
○ 4x + 8 = x+2
● VARIANCE
○ σ² = [(x - x+2)2 + (x+1 - x+2)2 + (x+2 - x+2)2 +(x+5 - x+2)2] / 4
○ σ² = [(x) + (-x-2)2] + [(x+1) + (-x-2)2] + [(x+2 + (-x-2)2] + [(x+5 + (-x-2)2] / 4
○ σ² = (-22 + -12 + 0 + 32) / 4
○ σ² = (4 + 1 + 0 + 9) / 4
○ σ² = (14) / 4
○ σ² = 3.5

I. What is the standard deviation of this set: {3.75, 3.8, 3.8, 5.2, 8.5}?

● MEAN
○ {3.75, 3.8, 3.8, 5.2, 8.5}
○ (3.75 + 3.8 + 3.8 + 5.2 + 8.5) / 5
○ (25.05) / 5 = 5.01
● VARIANCE
○ σ² = [(3.75 - 5.01)2 + (3.8 - 5.01)2 + (3.8 - 5.01)2 + (5.2 - 5.01)2 + (8.5 - 5.01)2] / 5
○ σ² = (1.59 + 1.46 + 1.46 + 0.04 + 12.18) / 5
○ σ² = 3.35
● STANDARD DEVIATION
○ σ = √3.35
○ σ = 1.83

J. The heights of 5 students are 156 cm, 176 cm, 157 cm, 169 cm and 167 cm. What is the
standard deviation of their heights?

● MEAN
○ {156, 157, 167, 169, 176}
○ (156 + 157 + 167 + 169 + 176) / 5 = 165
● VARIANCE
○ σ² = [(156 - 165)2 + (157 - 165)2 + (167 - 165)2 + (169 - 165)2 + (176 - 165)2] / 5
○ σ² = (81 + 64 + 4 + 16 + 121) / 5
○ σ² = 57.2

This document/presentation contains proprietary and confidential information. Reproduction, redistribution, or forwarding to any third party, in whole or in part, is
This study source wasstrictly prohibited
downloaded unless made with prior
by 100000848672578 fromwritten consent from
CourseHero.com Ayala Education
on 04-11-2023 Inc. Violation
20:36:28 GMT -05:00or noncompliance shall be dealt with according to law.

https://www.coursehero.com/file/158258222/mathematicssscspdf/
 ● STANDARD DEVIATION
○ σ = √57.2
○ σ = 7.56cm

K. The ages of the 7 grandchildren of Mrs. Mercado are: 7, 5, 3, 12, 6, 7 and 4 years old.
Compute for the standard deviation.

● MEAN
○ {3, 4, 5, 6, 7, 7, 12}
○ (3 + 4 + 5 + 6 + 7 + 7 + 12) / 7 = 6.29
● VARIANCE
○ σ² = [(3 - 6.29)2 + (4 - 6.29)2 + (5 - 6.29)2 + (6 - 6.29)2 + (7 - 6.29)2 + (7 - 6.29)2 +
(12 - 6.29)2] / 7
○ σ² = (10.82 + 5.24 + 1.66 + 0.08 + 0.50 + 0.50 + 32.60) / 7
○ σ² = 7.34
● STANDARD DEVIATION
○ σ = √7.34
○ σ = 2.71

L. Determine the standard deviation of Paulo’s grades in three quizzes: 88%, 98% and 86%.

● MEAN
○ {86%, 88%, 98%}
○ (0.86 + 0.88 + 0.98) / 3 = 0.91
● VARIANCE
○ σ² = [(0.86 - 0.91)2 + (0.88 - 0.91)2 + (0.98 - 0.91)2] / 3
○ σ² = (0.0025 + 0.0009 + 0.0049) / 3
○ σ² = 0.0028
● STANDARD DEVIATION
○ σ = √0.0028
○ σ = 0.053 or 5.3%

M. The mean of 5 consecutive integers is 6. What is the standard deviation?

SOLVE FOR THE VALUE OF x:

■ The MEAN of the 5 consecutive integers is 6

■ Let the 5 consecutive integers be:
- x, x+1, x+2, x+3, x+4, respectively

❏ 6 = (x + (x+1) + (x+2) + (x+3) + (x+4)) / 5

❏ 6 = (5x + 1 + 2 + 3 + 4) / 5

This document/presentation contains proprietary and confidential information. Reproduction, redistribution, or forwarding to any third party, in whole or in part, is
This study source wasstrictly prohibited
downloaded unless made with prior
by 100000848672578 fromwritten consent from
CourseHero.com Ayala Education
on 04-11-2023 Inc. Violation
20:36:28 GMT -05:00or noncompliance shall be dealt with according to law.

https://www.coursehero.com/file/158258222/mathematicssscspdf/
 ❏ 6 = (5x + 10) / 5
❏ 30 = 5x + 10
❏ 30 - 10 = 5x
❏ 20 = 5x
❏ x=4

SUBSTITUTE THE VALUE OF x:

● MEAN
○ [(x + (x+1) + (x+2) + (x+3) + (x+4)] / 5
○ [(4 + (4+1) + (4+2) + (4+3) + (4+4)] / 5
○ (4 + 5 + 6 + 7 + 8) / 5
○ 30 / 5 = 6 (the mean we are given)

● VARIANCE
○ σ² = [(4-6)2 + (5-6)2 + (6-6)2 + (7-6)2 + (8-6)2] / 5
○ σ² = (4 + 1 + 0 + 1 + 4) / 5
○ σ² = 2

● STANDARD DEVIATION
○ σ = √2
○ σ = 1.41

N. The mean of 7 consecutive integers is 10. What is the standard deviation?

SOLVE FOR THE VALUE OF x:

■ The MEAN of the 7 consecutive integers is 10

■ Let the 7 consecutive integers be:
- x, x+1, x+2, x+3, x+4, x+5, x+6 respectively

❏ 10 = (x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6)) / 7

❏ 10 = (7x + 1 + 2 + 3 + 4 + 5 + 6) / 7
❏ 10 = (7x + 21) / 7
❏ 70 = 7x + 21
❏ 70 - 21 = 7x
❏ 49 = 7x
❏ x=7

This document/presentation contains proprietary and confidential information. Reproduction, redistribution, or forwarding to any third party, in whole or in part, is
This study source wasstrictly prohibited
downloaded unless made with prior
by 100000848672578 fromwritten consent from
CourseHero.com Ayala Education
on 04-11-2023 Inc. Violation
20:36:28 GMT -05:00or noncompliance shall be dealt with according to law.

https://www.coursehero.com/file/158258222/mathematicssscspdf/
 SUBSTITUTE THE VALUE OF x:

● MEAN
○ [(x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6)] / 7
○ [(7 + (7+1) + (7+2) + (7+3) + (7+4) + (7+5) + (7+6)] / 7
○ (7 + 8 + 9 + 10 + 11 + 12 + 13) / 7
○ 70 / 7 = 10 (the mean we are given)

● VARIANCE
○ σ² = [(7-10)2 + (8-10)2 + (9-10)2 + (10-10)2 + (11-10)2 + (12-10)2 + (13-10)2]
/5
○ σ² = (9 + 4 + 1 + 0 + 1 + 4 + 9) / 7
○ σ² = 4

● STANDARD DEVIATION
○ σ = √4
○ σ=2

This document/presentation contains proprietary and confidential information. Reproduction, redistribution, or forwarding to any third party, in whole or in part, is
This study source wasstrictly prohibited
downloaded unless made with prior
by 100000848672578 fromwritten consent from
CourseHero.com Ayala Education
on 04-11-2023 Inc. Violation
20:36:28 GMT -05:00or noncompliance shall be dealt with according to law.

https://www.coursehero.com/file/158258222/mathematicssscspdf/
Powered by TCPDF (www.tcpdf.org)