Descriptive Statistics - GMAT Quantitative
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A high school basketball player practices 40 free throws every day. Over the past 90 days he has averaged 25 successful free throws.
What is the probability that tomorrow he will make 30 or more free throws?
A high school basketball player practices 40 free throws every day. Over the past 90 days he has averaged 25 successful free throws.
What is the probability that tomorrow he will make 30 or more free throws?
standard deviation =
Percentile =
standard deviation =
Percentile =
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We think that our average customer spends roughly $40 - $60 every time he/she visits our website. We can assume that the expenditure amounts are normally distributed, but, we do not know the standard deviation. We sample 15 web expenditures; our sample average is $52 and our sample standard deviation is $8.
We are 95% sure that our true population average is $52 plus or minus....
We think that our average customer spends roughly $40 - $60 every time he/she visits our website. We can assume that the expenditure amounts are normally distributed, but, we do not know the standard deviation. We sample 15 web expenditures; our sample average is $52 and our sample standard deviation is $8.
We are 95% sure that our true population average is $52 plus or minus....
standard deviation of the sample mean is:
95% 
for 14 d.o.f. =
confidence interval is
standard deviation of the sample mean is:
95%
confidence interval is
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Calculate the average of the set of numbers.
Statement 1: the range of the set is 13
Statement 2: the mode of the set is 16
Calculate the average of the set of numbers.
Statement 1: the range of the set is 13
Statement 2: the mode of the set is 16
To answer this question, we must understand the vocabulary. The range of a set is the difference between the largest and smallest numbers. The mode of a set is the number which comes up most frequently. Neither the range nor the mode, nor both, will help us solve for the average, however.
To answer this question, we must understand the vocabulary. The range of a set is the difference between the largest and smallest numbers. The mode of a set is the number which comes up most frequently. Neither the range nor the mode, nor both, will help us solve for the average, however.
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The average score on a statistics test is 70%. The standard deviation is 10%.
What is the minimal test score that Judy needs in order to reach the 90th percentile?
The average score on a statistics test is 70%. The standard deviation is 10%.
What is the minimal test score that Judy needs in order to reach the 90th percentile?
One tailed test (Z table)
In English - Judy must be at least 1.28 standard deviations above the average.
One tailed test (Z table)
In English - Judy must be at least 1.28 standard deviations above the average.
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Our final sales figures (in millions) for the year are:
Use Excel to calculate the correlation coefficient between the month number
etc.
and the sales figure(s).
Also, compute the 
value for testing the confidence level for the correlation coefficient.
Our final sales figures (in millions) for the year are:
Use Excel to calculate the correlation coefficient between the month number
etc.
and the sales figure(s).
Also, compute the
Excel indicates the correlation coefficient 
is
the formula for 
is -
Excel indicates the correlation coefficient
the formula for
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Our final sales figures (in millions) for the year are:
Using the above data, calculate the regression line
that best fits the data.
Hint – make the month number
etc.
the independent variable 
and make the sales figure the dependent variable 
. Use Excel to calculate the slope.
Our final sales figures (in millions) for the year are:
Using the above data, calculate the regression line
that best fits the data.
Hint – make the month number
etc.
the independent variable
Excel indicates the slope is
Excel indicates the slope is
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The average sales price of a home in Ourtown U.S.A. is $120,000.
The population standard deviation is $20,000.
What is the probability that the next home will sell for more than $130,000?
The average sales price of a home in Ourtown U.S.A. is $120,000.
The population standard deviation is $20,000.
What is the probability that the next home will sell for more than $130,000?
z=
translates to:
percentile (below) and
percentile (above).
z=
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A data set comprises a large number of entries. What is the interquartile range of the set?
Statement 1: The 75th percentile is 745
Statement 2: The median is 556
A data set comprises a large number of entries. What is the interquartile range of the set?
Statement 1: The 75th percentile is 745
Statement 2: The median is 556
Two things are needed to calculate the interquartile range - the first quartile and the third quartile (the median is irrelevant). Statement 1 gives you the latter (the third quartile, by definition, is the 75th percentile) but neither gives you the former.
Two things are needed to calculate the interquartile range - the first quartile and the third quartile (the median is irrelevant). Statement 1 gives you the latter (the third quartile, by definition, is the 75th percentile) but neither gives you the former.
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We are trying to determine the average age of the Cardinal baseball fan. We know that the age distribution of Cardinal nation is normally distributed with a standard deviation of 20. We need to determine the average age. We take a sample of 40 fans and the average of our sample is 42 years old.
What is the 95% confidence interval (range) for our sample average of 42? (remember – confidence intervals are always 2- tailed (plus or minus)).
We are trying to determine the average age of the Cardinal baseball fan. We know that the age distribution of Cardinal nation is normally distributed with a standard deviation of 20. We need to determine the average age. We take a sample of 40 fans and the average of our sample is 42 years old.
What is the 95% confidence interval (range) for our sample average of 42? (remember – confidence intervals are always 2- tailed (plus or minus)).
The z value for 95th percentile is:
the sample standard deviation is:
The z value for 95th percentile is:
the sample standard deviation is:
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We are trying to determine the average age of the Cardinal baseball fan. We know that the age distribution of Cardinal nation is normally distributed with a standard deviation of 20. We need to determine the average age. We take a sample of 40 fans and the average of our sample is 42 years old.
However, the Cardinal President of Operations wants a 98% confidence interval of plus or minus 5.0. What sample size do we need to satisfy his request?
We are trying to determine the average age of the Cardinal baseball fan. We know that the age distribution of Cardinal nation is normally distributed with a standard deviation of 20. We need to determine the average age. We take a sample of 40 fans and the average of our sample is 42 years old.
However, the Cardinal President of Operations wants a 98% confidence interval of plus or minus 5.0. What sample size do we need to satisfy his request?
solve for 
solve for
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The Cardinals average 4 extra inning games per month.
What is the probability that they will have more than 4 extra inning games next month? Hint – Poisson distribution.
The Cardinals average 4 extra inning games per month.
What is the probability that they will have more than 4 extra inning games next month? Hint – Poisson distribution.
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A real estate tycoon wants to test the hypothesis that the percentage of people who own their own home in Florida is the same as the home ownership percentage in Georgia. He states his null hypothesis as 'the Florida percentage is the same as the Georgia percentage' and the alternative hypothesis is 'the percentages are significantly different'. He decides on a 2-tailed test and he samples 400 Florida homes and 600 Georgia homes. His sample results:
Florida - 280 homeowners out of 400 (.7)
Georgia - 384 homeowners out of 600 (.64)
a percentage difference of .06
What is the lowest confidence percentage that will support his rejection of the null hypothesis? Stated another way – what is the highest percentage that will support his acceptance of the null hypothesis?
A real estate tycoon wants to test the hypothesis that the percentage of people who own their own home in Florida is the same as the home ownership percentage in Georgia. He states his null hypothesis as 'the Florida percentage is the same as the Georgia percentage' and the alternative hypothesis is 'the percentages are significantly different'. He decides on a 2-tailed test and he samples 400 Florida homes and 600 Georgia homes. His sample results:
Florida - 280 homeowners out of 400 (.7)
Georgia - 384 homeowners out of 600 (.64)
a percentage difference of .06
What is the lowest confidence percentage that will support his rejection of the null hypothesis? Stated another way – what is the highest percentage that will support his acceptance of the null hypothesis?
standard deviation =
0.06 is 2.0 standard deviations from the assumed difference of 0. A z value of 2.0 shows a 1-tailed percentage of .9772 – which is equal to a 2-tailed percentage of .9544
standard deviation =
0.06 is 2.0 standard deviations from the assumed difference of 0. A z value of 2.0 shows a 1-tailed percentage of .9772 – which is equal to a 2-tailed percentage of .9544
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A data set comprises 1,000 entries. What is its interquartile range?
Statement 1: The 75th percentile is 64.
Statement 2: The 25th percentile is 30.
A data set comprises 1,000 entries. What is its interquartile range?
Statement 1: The 75th percentile is 64.
Statement 2: The 25th percentile is 30.
The interquartile range is the difference between the third and first quartiles - that is, the 75th percentile and the 25th percentile. Knowing both is necessary and sufficient.
The interquartile range is the difference between the third and first quartiles - that is, the 75th percentile and the 25th percentile. Knowing both is necessary and sufficient.
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The average age of our customers is 40 years with a standard deviation of 10 years.
What is the probability that the next customer to enter our store will be between 30 and 50 years old ?
The average age of our customers is 40 years with a standard deviation of 10 years.
What is the probability that the next customer to enter our store will be between 30 and 50 years old ?
The range of 30-50 is plus or minus 1 standard deviation.
The 
value for +1 standard deviation is
the 
value for -1 standard deviation is
The range of 30-50 is plus or minus 1 standard deviation.
The
the
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We randomly sampled 175 people in Our Town USA and found that 62.9% of them favored Coke over Pepsi. We decided on a 90% 2 tailed test (z=1.64) and proclaimed that we were 90% confident of the 62.9% plus or minus 6%.
We arrived at the 6% by first calculating the standard deviation:
and then multiplying .0365 by z (1.64)
What sample size do we need to be plus or minus 4%?
We randomly sampled 175 people in Our Town USA and found that 62.9% of them favored Coke over Pepsi. We decided on a 90% 2 tailed test (z=1.64) and proclaimed that we were 90% confident of the 62.9% plus or minus 6%.
We arrived at the 6% by first calculating the standard deviation:
and then multiplying .0365 by z (1.64)
What sample size do we need to be plus or minus 4%?
sample size =
sample size =
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The Z Table is the cornerstone of intro stats. It translates the 'number of standard deviations from the mean' into a percentile (.90, .95. .99. etc.). The table is laid out with the assumption that the test being conducted is a 'one-way' test, meaning that the Z value is greater than some percentile (if Z is positive) or less than some percentile (if Z is negative). Another way of saying this is: the Z table only measures the area under the curve for 1 of the 'tails' (either the extreme right or the extreme left). So, if we have a 2 tailed test for say 95% confidence, then we must put 2.5% in our right tail and 2.5% in our left tail. Conversely, a one tailed test for 95% puts 5% in the right tail only.
Arrange the 5 following confidence intervals in ascending (lowest to highest) order of their Z value:
A) 2 tailed test at 95%
B) 1 tailed test at 95%
C) 1 tailed test at 90%
D) 2 tailed test at 99%
E) 1 tailed test at 99%
The Z Table is the cornerstone of intro stats. It translates the 'number of standard deviations from the mean' into a percentile (.90, .95. .99. etc.). The table is laid out with the assumption that the test being conducted is a 'one-way' test, meaning that the Z value is greater than some percentile (if Z is positive) or less than some percentile (if Z is negative). Another way of saying this is: the Z table only measures the area under the curve for 1 of the 'tails' (either the extreme right or the extreme left). So, if we have a 2 tailed test for say 95% confidence, then we must put 2.5% in our right tail and 2.5% in our left tail. Conversely, a one tailed test for 95% puts 5% in the right tail only.
Arrange the 5 following confidence intervals in ascending (lowest to highest) order of their Z value:
A) 2 tailed test at 95%
B) 1 tailed test at 95%
C) 1 tailed test at 90%
D) 2 tailed test at 99%
E) 1 tailed test at 99%
C) 1 tailed test at 90% - 1.28
B) 1 tailed test at 95% - 1.645
A) 2 tailed test at 95% - 1.96
E) 1 tailed test at 99% - 2.33
D) 2 tailed test at 99% - 2.58
C) 1 tailed test at 90% - 1.28
B) 1 tailed test at 95% - 1.645
A) 2 tailed test at 95% - 1.96
E) 1 tailed test at 99% - 2.33
D) 2 tailed test at 99% - 2.58
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Ben is given a simple stats problem. Of the 1,000 students at Our Town Community College, 600 are female, 400 are male. The problem asks: if we select 20 students at random, what is the probability that our sample of 20 will contain 10 or 11 or 12 or 13 females.
The simple solution is to go to the binomial table and add up the 4 probabilities of 10, 11, 12 and 13 with a population percentage of 0.6:
However, Ben likes to do things the hard way. He decides to use the normal distribution as an approximation to the binomial. Why? No one knows why. Ben is just Ben.
He gets the Z value and percentile for 9.5 and then obtains the Z value and percentil value for 13.5. He then subtracts the 9.5 percentile from the 13.5 percentile and hopefully ends up with something close to .6224
What is:
the Z value for 9.5
the percentile for 9.5
the Z value for 13.5
the percentile for 13.5
Ben is given a simple stats problem. Of the 1,000 students at Our Town Community College, 600 are female, 400 are male. The problem asks: if we select 20 students at random, what is the probability that our sample of 20 will contain 10 or 11 or 12 or 13 females.
The simple solution is to go to the binomial table and add up the 4 probabilities of 10, 11, 12 and 13 with a population percentage of 0.6:
However, Ben likes to do things the hard way. He decides to use the normal distribution as an approximation to the binomial. Why? No one knows why. Ben is just Ben.
He gets the Z value and percentile for 9.5 and then obtains the Z value and percentil value for 13.5. He then subtracts the 9.5 percentile from the 13.5 percentile and hopefully ends up with something close to .6224
What is:
the Z value for 9.5
the percentile for 9.5
the Z value for 13.5
the percentile for 13.5
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Seven kids in a kindergarten class have the following ages:
.
Amy and Lilly join this kindergarten class. What is the range of the nine kids' ages?
(1) Amy is 
years old.
(2) The sum of the ages of both kids is 
.
Seven kids in a kindergarten class have the following ages:
Amy and Lilly join this kindergarten class. What is the range of the nine kids' ages?
(1) Amy is
(2) The sum of the ages of both kids is
Statement (1) alone does not give us any information to find out the age of Lilly, therefore it is not sufficient.
Statement (2) alone does not give us enough information to determine the ages of each kid. Therefore it is not sufficient.
Statement (1) and (2) give us the following information:
A = 6 and A + L = 13, therefore L = 13 - 6 = 7
With the ages of both kids we can find the new age range = 8 - 2 = 6
Statement (1) alone does not give us any information to find out the age of Lilly, therefore it is not sufficient.
Statement (2) alone does not give us enough information to determine the ages of each kid. Therefore it is not sufficient.
Statement (1) and (2) give us the following information:
A = 6 and A + L = 13, therefore L = 13 - 6 = 7
With the ages of both kids we can find the new age range = 8 - 2 = 6
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What is the value of 
in the list above?
(1) The range of the numbers in the list is 
.
(2) 
What is the value of
(1) The range of the numbers in the list is
(2)
Statement (1) indicates that the range of the numbers is 20. The range is the difference between the highest number and the lowest number. The difference between each pair of numbers in the list is less than 20. Therefore, n is the lowest number in the list. We can then calculate n as follows:
Therefore Statement (1) is SUFFICIENT.
Statement (2) states that n<5 which means n is the lowest number in the list. However this information alone is not sufficient to find the value of n.
Therefore Statement (2) is not SUFFICIENT.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
Statement (1) indicates that the range of the numbers is 20. The range is the difference between the highest number and the lowest number. The difference between each pair of numbers in the list is less than 20. Therefore, n is the lowest number in the list. We can then calculate n as follows:
Therefore Statement (1) is SUFFICIENT.
Statement (2) states that n<5 which means n is the lowest number in the list. However this information alone is not sufficient to find the value of n.
Therefore Statement (2) is not SUFFICIENT.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
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What is the range of the numbers in the list above?
(1) 
.
(2) 
.
What is the range of the numbers in the list above?
(1)
(2)
The range of a set of numbers is the difference between the maximum and the minimum values of these numbers. In order to determine the range of these numbers, we need to know the values of n and 2n-1 or at least we should know that n and 2n-1 are not the minimum or the maximum values, meaning n and 2n-1 do not affect the range of these numbers.
(1) 
Therefore n is not the minimum value in this list. However, we do not if 2n-1 is the maximum value. Statement (1) ALONE is not sufficient.
(2) 
n and 2n-1 do not affect the range then. The range of these numbers is:
Statement (2) ALONE is sufficient.
The range of a set of numbers is the difference between the maximum and the minimum values of these numbers. In order to determine the range of these numbers, we need to know the values of n and 2n-1 or at least we should know that n and 2n-1 are not the minimum or the maximum values, meaning n and 2n-1 do not affect the range of these numbers.
(1)
Therefore n is not the minimum value in this list. However, we do not if 2n-1 is the maximum value. Statement (1) ALONE is not sufficient.
(2)
n and 2n-1 do not affect the range then. The range of these numbers is:
Statement (2) ALONE is sufficient.
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