Chapter 3 Stats
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 orless, 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 orless, 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