Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

In the data set below, what is the variance? $\newline$ $7, 1, 5, 2, 5, 5, 3$ $\newline$ If the answer is a decimal, round it to the nearest tenth. $\newline$ variance $(\sigma^2)$ : _____

View step-by-step help

View step-by-step help

Variance and standard deviation

Full solution

Q. In the data set below, what is the variance?

\newline

7, 1, 5, 2, 5, 5, 3

\newline

If the answer is a decimal, round it to the nearest tenth.

\newline

variance

(\sigma^2)

: _____

Calculate Squared Differences: Now that we have the mean, we calculate the squared differences from the mean for each data point. $\newline$ $(7 - 4)^2 + (1 - 4)^2 + (5 - 4)^2 + (2 - 4)^2 + (5 - 4)^2 + (5 - 4)^2 + (3 - 4)^2$ $\newline$ $= 3^2 + (-3)^2 + 1^2 + (-2)^2 + 1^2 + 1^2 + (-1)^2$ $\newline$ $= 9 + 9 + 1 + 4 + 1 + 1 + 1$ $\newline$ $= 26$
Find Variance: Finally, we divide the sum of squared differences by the number of data points to find the variance. $\newline$ $\Sigma(x_i - \mu)^2 = 26$ $\newline$ $N = 7$ $\newline$ Variance $\sigma^2 = (\Sigma(x_i - \mu)^2)/N$ $\newline$ $\sigma^2 = 26/7$ $\newline$ $\sigma^2 \approx 3.71428571429$ $\newline$ Rounded to the nearest tenth: $\sigma^2 \approx 3.7$

More problems from Variance and standard deviation

Question

Select the outlier in the data set.

33

43

49

57

62

67

81

561

Posted 2 months ago

Question

In the data set below, what is the variance?

\newline

8

7

6

4

3

\newline

If the answer is a decimal, round it to the nearest tenth.

\newline

\sigma^2

Posted 3 months ago

Question

What is the mode?

\newline

7, 8, 8, 7, 5, 7

Posted 3 days ago

Question

In the data set below, what are the lower quartile, the median, and the upper quartile?

\newline

1

2

2

2

2

4

4

5

7

7

\newline

=

\newline

=

\newline

=

Posted 2 months ago

Question

In the data set below, what are the lower quartile, the median, and the upper quartile?

1,2,2,2,2,4,4,5,7,7

lower quartile =

\underline{\hspace{1cm}}

\underline{\hspace{1cm}}

upper quartile =

\underline{\hspace{1cm}}

Posted 2 months ago

Question

Jerry has a large car which holds

22

gallons of fuel and gets

20

miles per gallon. Kate has a smaller car which holds

16

5

gallons of fuel and gets

30

miles per gallon. If both cars have a full tank of fuel now and drive the same distance, in how many miles will the remaining fuel in each tank be the same?

\newline

1

\newline

320

\newline

325

\newline

330

\newline

335

Posted 1 month ago

Question

3

more books than Topher did over their summer vacation. If Rachel read

7

books, how many books did Topher read?

\newline

1

\newline

3

\newline

4

\newline

7

\newline

10

Posted 2 months ago

Question

Lilia wants to exchange US dollars for Euros before traveling to France. Her bank offers her an exchange rate of

1

0

84

Euros. Approximately how many US dollars does Lilia need to exchange if she wants to receive

350

Euros from her bank?

\newline

1

\newline

\mathbf{2 6 6}

\newline

294

\newline

417

\newline

434

Posted 4 months ago

Question

Petra waited in line for

78

minutes for tickets to see her favorite band. How long did she wait in hours?

\newline

1

\newline

0

8

\newline

1

1

\newline

1

3

\newline

1

5

Posted 4 months ago

Question

A frozen pepperoni pizza has

6

servings. If the pizza contains a total of

1

860

calories, what is the number of calories per serving?

\newline

1

\newline

1

860

\newline

930

\newline

465

\newline

310

Posted 4 months ago