Chapter 3 Stats

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The standard deviation can be negative.

False

The standard deviation is a resistant measure of spread.

False

The median for the given set of six ordered data values is 27.5 What is the missing​ value? 9, 12, 23, ___, 41, 50

Out of the 6 numbers.... Mean = 6 x4 = missing value 27.5 (x3-x4)/2 = 27.5 (23 - x4)/2 = 27.5 x4 = (27.5*2) - 23 x4 = 32

​_______ divide data sets in fourths.

Quarties

True or​ False: When comparing two​ populations, the larger the standard​ deviation, the more dispersion the distribution​ has, provided that the variable of interest from the two populations has the same unit of measure.

True, because the standard deviation describes how​ far, on​ average, each observation is from the typical value. A larger standard deviation means that observations are more distant from the typical​ value, and​ therefore, more dispersed.

When an observation that is much larger than the rest of the data is added to a data​ set, the value of the mean will

increase

For a distribution that is skewed​ right, the median is

left of center of the box.

zipcode

qualitiative

For a distribution that is​ symmetric, the left whisker is

the same length as the right whisker.

The sum of the deviations about the mean always equals

zero

For a distribution that is skewed​ left, the left whisker is

longer than the right whisker.

For a distribution that is skewed​ left, which of the following is​ true?

mean<median

For a distribution that is symmetric, which of the following is true?

mean=median

For a distribution that is skewed​ right, which of the following is​ true?

mean>median

In a​ boxplot, if the median is to the left of the center of the box and the right whisker is substantially longer than the left​ whisker, the distribution is skewed

right

Are any of the measures of dispersion among the​ range, the​ variance, and the standard​ deviation, resistant? Explain.

​No, all of these measures of dispersion are affected by extreme values.

The Empirical Rule

​· Approximately​ 68% of the data will lie within 1 standard deviation of the mean. ​· Approximately​ 95% of the data will lie within 2 standard deviations of the mean. ​· Approximately​ 99.7% of the data will lie within 3 standard deviations of the mean

Which of the accompanying boxplots likely has the data with the larger standard​ deviation? Why?

Boxplot II likely has the data with the larger standard deviation because the boxplot appears to have a greater​ spread, which likely results in a larger standard deviation.

What does it mean if a statistic is​ resistant?

Extreme values​ (very large or​ small) relative to the data do not affect its value substantially.

True or​ False: A data set will always have exactly one mode.

False

When an observation that is much larger than the rest of the data is added to a data​ set, the value of the median will increase substantially.

False

Which histogram depicts a higher standard​ deviation?

Histogram a depicts the higher standard​ deviation, because the distribution has more dispersion.

A professor has recorded exam grades for 20 students in his​ class, but one of the grades is no longer readable. If the mean score on the exam was 81 and the mean of the 19 readable scores is 84​, what is the value of the unreadable​ score?

Mean for 20 = 81 Mean for 19 = 84 (20*81) - (19*84) = 24 The value of the unreadable score is 24

If the standard deviation of a variable is 5​, what is the​ variance

25

A highly selective boarding school will only admit students who place at least 2 standard deviations above the mean on a standardized test that has a mean of 300 and a standard deviation of 26. What is the minimum score that an applicant must make on the test to be​ accepted?

353 u +2o

a) The 5th percentile of the weight of males 36 months of age in a certain city is 13.0 kg.

5​% of ​36-month-old males weigh 13.0 kg or​less, and 95​% of​ 36-month-old males weigh more than 13.0 kg.

If the variance of a variable is 64​, what is the standard​ deviation?

8

The 90th percentile of the length of newborn females in a certain city is 53.8 cm.

90​% of newborn females have a length of 53.8 cm or​less, and 10​% of newborn females have a length that is more than 53.8 cm.

z score excel

=(DataPoint-AVERAGE(DataSet))/STDEV(DataSet)

If a variable has a distribution that is​ bell-shaped with mean 29 and standard deviation 3​, then according to the Empirical​ Rule, 95.0​% of the data will lie between which​ values?

According to the Empirical​ Rule, 95.0​% of the data will lie between 23 and 35. 68% = o +/- u 95% = o +/- 2u 99.7% = o +/- 3u

What can be said about a set of data with a standard deviation of​ 0?

All the observations are the same value.

z score

The​ _______ represents the number of standard deviations an observation is from the mean.

On the basis of the histogram to the​ right, comment on the appropriateness of using the Empirical Rule to make any general statements about the weights of the candies

The histogram is approximately​ bell-shaped so the Empirical Rule can be used.

For the distribution​ shown, which letter represents the​ mode?

The left line

A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be​ larger, the mean or the​ median? Why?

The mean will likely be larger because the extreme values in the right tail tend to pull the mean in the direction of the tail.

For the distribution​ shown, which letter represents the​ median?

The middle line

Discuss limitations of the range as a measure of dispersion.

The range only takes into account the smallest and largest​ values, which does not provide any information about the dispersion of the distribution between those values.

For the distribution​ shown, which letter represents the​ mean?

The right line


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