II. Fill in the blanks to complete the following sentences. Choose your answer from the word pool.
a. variance
b. less scattered
c. mode
d. less reliable
e. mean
f. median
g. range
h. variability
i. small
j. standard deviation
k. large
I. more scattered
m. average deviation
n. more reliable
31. The measure of central tendency to use best when there are no extreme values is the _________
32. ________is the most appropriate to use in describing a non-numerical set of data.
33. Whenever there is any extreme value in a set of data,______ is the best measure of central tendency to apply in describing such data.
34. Measures of ______are used to determine how spread out or scattered the values are in a data set.
35. If the variability is________ then the data values are more scattered or spread out. If the variability is lesser, then the data values are less scattered or spread out.
36. The________ is not a perfect measure of variability, since it ignores the data values in between the highest and the lowest.
37. The __________is also not a perfect measure of variability to use since the absolute value is involved in calculating it, resulting to a little inconvenience because case-by-case analysis and a little of higher mathematics concepts might be needed at some point.
38. The________ is also not convenient to use because the process of working for it produces large numbers due to squaring.
39. The________ is the most reliable measure of variability.
40. The lesser the variability, the _______is the mean.
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Step-by-step explanation:
Formulas for the Sample Standard Deviation
s
=
√
∑
(
x
−
¯¯¯
x
)
2
n
−
1
or
s
=
√
∑
f
(
x
−
¯¯¯
x
)
2
n
−
1
For the sample standard deviation, the denominator is
n
–
1
, that is the sample size MINUS
1
.
Formulas for the Population Standard Deviation
σ
=
√
∑
(
x
−
μ
)
2
N
or
σ
=
√
∑
f
(
x
−
μ
)
2
N
For the population standard deviation, the denominator is
N
, the number of items in the population.
In these formulas,
f
represents the frequency with which a value appears. For example, if a value appears once,
f
is one. If a value appears three times in the data set or population,
f
is three.
Sampling Variability of a Statistic
How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example of a standard error. It is a special standard deviation and is known as the standard deviation of the sampling distribution of the mean. You will cover the standard error of the mean when you learn about The Central Limit Theorem (not now). The notation for the standard error of the mean is
σ
√
n
where
σ
is the standard deviation of the population and
n
is the size of the sample.