Chapter 2: Q58E (page 103)

Calculate the variance and standard deviation for samples where
a.n= 10, ∑x² = 84, ∑x= 20
b.n= 40, ∑x² = 380, ∑x= 100
c.n= 20, ∑x² = 18, ∑x= 17.

Short Answer

Expert verified

Variance = 8.88, Standard Deviation = 2.98
Variance = 9.58, Standard Deviation = 3.09
Variance = 0.91, Standard Deviation = 0.95

Step by step solution

Calculating the variance and standard deviation for a

Given: n= 10, ∑x² = 84, ∑x= 20

$M e a n = \frac{\sum x}{n} = \frac{20}{10} = 2 {\bar{x}}^{2} = 4$

$S a m p l e V a r i a n c e = \frac{\sum x^{2} - {\bar{x}}^{2}}{n - 1} = \frac{84 - 4}{10 - 1} = \frac{80}{9} = 8.88$

localid="1662206428948" $\begin{array}{rcl} Sample standard deviation & = & \sqrt{Sample variance} \\ = & \sqrt{8.88} \\ = & 2.98 \end{array}$

Therefore, variance is 8.88 and standard deviation is 2.98.

Computing the variance and standard deviation for b

Given: n= 40, ∑x² = 380, ∑x= 100

$M e a n = \frac{\sum x}{n} = \frac{100}{40} = 2.5 {\bar{x}}^{2} = 6.25$

$S a m p l e V a r i a n c e = \frac{\sum x^{2} - {\bar{x}}^{2}}{n - 1} = \frac{380 - 6.25}{40 - 1} = \frac{373.75}{39} = 9.58$

$Samplestandarddeviation = \sqrt{Samplevariance} = \sqrt{9.58} = 3.09$

Therefore, variance = 9.58 and standard deviation = 3.09.

Finding the variance and standard deviation for c

Given: n= 20, ∑x² = 18, ∑x= 17.

$M e a n = \frac{\sum x}{n} = \frac{17}{20} = 0.85 {\bar{x}}^{2} = 0.7225$

$SampleVariance = \frac{\sum x^{2} - {\bar{x}}^{2}}{n - 1} = \frac{18 - 0.7225}{20 - 1} = \frac{17.2775}{19} = 0.91$

$Samplestandarddeviation = \sqrt{Samplevariance} = \sqrt{0.91} = 0.95$

Therefore, Variance and Standard Deviation are 0.91 and 0.95 respectively.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Calculate the variance and standard deviation for samples where
a.n= 10, ∑x² = 84, ∑x= 20
b.n= 40, ∑x² = 380, ∑x= 100
c.n= 20, ∑x² = 18, ∑x= 17.

Short Answer

Step by step solution

Calculating the variance and standard deviation for a

Computing the variance and standard deviation for b

Finding the variance and standard deviation for c

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Decision Maths

Pure Maths

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Calculate the variance and standard deviation for samples wherea.n= 10, ∑x2 = 84, ∑x= 20b.n= 40, ∑x2 = 380, ∑x= 100c.n= 20, ∑x2 = 18, ∑x= 17.

Short Answer

Step by step solution

Calculating the variance and standard deviation for a

Computing the variance and standard deviation for b

Finding the variance and standard deviation for c

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Decision Maths

Pure Maths

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Calculate the variance and standard deviation for samples where
a.n= 10, ∑x² = 84, ∑x= 20
b.n= 40, ∑x² = 380, ∑x= 100
c.n= 20, ∑x² = 18, ∑x= 17.