Question

Consider the following.

*n* = 8 measurements: 1, 2, 4, 1, 2, 4, 3, 2

Calculate the sample variance, *s*^{2}, using the
definition formula. (Round your answer to four decimal places.)

*s*^{2} =

Calculate the sample variance,

*s*^{2}

using the computing formula. (Round your answer to four decimal places.)

*s*^{2} =

Calculate the sample standard deviation, *s*. (Round your
answer to three decimal places.)

* s* =

Answer #1

TOPIC:Sample variance and sample standard deviation.

Consider the following.
n = 8
measurements: 4, 3, 7, 7, 5, 5, 4, 6
Calculate the sample variance, s2, using the
definition formula. (Round your answer to four decimal places.)
s2 =
Calculate the sample variance, s2 using the
computing formula. (Round your answer to four decimal places.)
s2 =
Find the sample standard deviation, s. (Round your
answer to three decimal places.)
s =

You are given
n = 5
measurements: 3, 1, 4, 5, 5.
(a) Calculate the sample mean,
x.
x =
(b) Calculate the sample variance, s2, using
the formula given by the definition.
s2 =
(c) Find the sample standard deviation, s. (Round your
answer to three decimal places.)
s =
(d) Find s2 and s using the computing
formula. (Round your answer for s to three decimal
places.)
s2 =
s =
Compare the results with those found in...

Consider the data.
xi
1
2
3
4
5
yi
2
8
6
11
13
(a)
Compute the mean square error using
equation s2 = MSE =
SSE
n −
2
. (Round your answer to two decimal places.)
(b)
Compute the standard error of the estimate using equation
s =
MSE
=
SSE
n −
2
. (Round your answer to three decimal places.)
(c)
Compute the estimated standard deviation of
b1
using equation
sb1 =
s
Σ(xi −
x)2...

Consider the data set.
2, 4, 6, 7, 8
(a) Find the range. (Enter an exact number.)
(b) Use the defining formula to compute the sample standard
deviation s. (Enter a number. Round your answer to two
decimal places.)
(c) Use the defining formula to compute the
population standard deviation σ. (Enter a number. Round
your answer to two decimal places.)

Consider the data set. 2, 3, 4, 6, 9
(a) Find the range.
b) Use the defining formula to compute the sample standard
deviation s. (Round your answer to two decimal places.)
(c) Use the defining formula to compute the population standard
deviation σ. (Round your answer to two decimal places.)

Consider the following recursive equation s(2n) = 2s(n) + 3;
where n = 1, 2, 4, 8, 16, ...
s(1) = 1
a. Calculate recursively s(8)
b. Find an explicit formula for s(n)
c. Use the formula of part b to calculate s(1), s(2), s(4), and
s(8)
d Use the formula of part b to prove the recurrence equation
s(2n) = 2s(n) + 3

Consider the following frequency distribution.
Class
Frequency
2 up to 4
14
4 up to 6
66
6 up to 8
74
8 up to 10
14
a. Calculate the population mean.
(Round your answer to 2 decimal places.)
Population mean
b. Calculate the population variance and the
population standard deviation. (Round intermediate
calculations to at least 4 decimal places and final answers to 2
decimal places.)
Population
variance
Population standard deviation

An article in an archaeological science journal described 26
samples of pottery found at four different kiln sites in a certain
country. The percentage of iron oxide in each of five samples
collected at one particular site was as follows.
1.35 2.60 1.57 2.13 1.62
(a)
Calculate the range.
(b)
Calculate the sample variance and the standard deviation using
the computing formula. (Round your answers to four decimal
places.)
s2
=
s
=
(c)
Compare the range and the standard deviation. The range is...

The following measurements (in picocuries per liter) were
recorded by a set of ozone detectors installed in a laboratory
facility:
201.9,203.6,264.1,235.6,221.1 Using these measurements,
construct a 90% confidence interval for the mean level of ozone
present in the facility. Assume the population is approximately
normal.
Copy Data
Step 1 of 4:
Calculate the sample mean for the given sample data. Round your
answer to two decimal places.
Step 2 of 4:
Calculate the sample standard deviation for the given sample...

An expert reviews a sample of 10 scientific articles (n = 10)
and records the following number of errors in each article: 0, 5,
4, 1, 2, 1, 3, 8, 0, and 7. Compute SS, variance, and standard
deviation for this sample using the definitional and computational
formula. (Round your answers to two decimal places.)
SS
variance
standard deviation

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