1
Hannah noted the height of each student in her class and found that the
mean height of the students is 56 inches, with a standard deviation of 1.2
inches. The height of one of the students, James, is 59 inches.
What is the z-score for James' height?
2.5
-2.5
3.6
-3.6
RATIONALE
Recall that the z-score can be calculated with the following formula:
The given value is 59 inches, the mean is 56 inches, and the standard deviation is 1.2
inches. Plug these values in to get the following z-score:
This also tells us that 59 is 2.5 z-scores or standard deviations above the mean.
CONCEPT
Standard Scores and Z-Scores
2
Which of the following is NOT a step used in calculating standard
deviation?
Subtracting the value of each data set from the mean.
Dividing the sum of each value by the total number of values plus 1.
, Calculating the mean of the data set.
Squaring the difference of x - u.
RATIONALE
Recall the standard deviation . So there is no addition of 1 to any values.
CONCEPT
Standard Deviation
3
In which of these cases should the median be used?
When the data has small variance
When the data has extreme values
When the data has nominal values
When data has no outliers
RATIONALE
Since the mean uses the actual values in the data, it is most affected by outliers and
skewness. So, we only want to use the mean when the data is symmetric as a measure
of centrality. When the data is skewed or has extreme values,
the median is a better measure since it is not as sensitive to these values.
CONCEPT
Measures of Center
4
The average daily rainfall for the past week in the town of Hope Cove is
normally distributed, with a mean rainfall of 2.1 inches and a standard
deviation of 0.2 inches.
If the distribution is normal, what percent of data lies between 1.9
inches and 2.3 inches of rainfall?
95%
,
34%
99.7%
68%
RATIONALE
Recall that if the data is normal, then the 68-95-99.7 rule applies which states that 68%
of all data points fall within one standard deviation of the mean, 95% of all data points
fall within two standard deviations of the mean, and 99.7% of all data points fall within
three standard deviations of the mean.
1.9 inches and 2.3 inches are both 0.2 inches from the mean of 2.1 inches, which is the
same as one standard deviation in either direction. This tells us that 68% of the data
should lie between 1.9 inches to 2.3 inches.
CONCEPT
68-95-99.7 Rule
5
Ralph records the time it takes for each of his classmates to run around the
track one time. As he analyzes the data on the graph, he notices very little
variation between his classmates’ times.
Which component of data analysis is Ralph observing?
The overall spread of the data
The center of the data set
An outlier in the data set
The overall shape of the data
RATIONALE
Since Ralph is looking at the variation of data, this is examining the spread of the data.
CONCEPT
Data Analysis
Hannah noted the height of each student in her class and found that the
mean height of the students is 56 inches, with a standard deviation of 1.2
inches. The height of one of the students, James, is 59 inches.
What is the z-score for James' height?
2.5
-2.5
3.6
-3.6
RATIONALE
Recall that the z-score can be calculated with the following formula:
The given value is 59 inches, the mean is 56 inches, and the standard deviation is 1.2
inches. Plug these values in to get the following z-score:
This also tells us that 59 is 2.5 z-scores or standard deviations above the mean.
CONCEPT
Standard Scores and Z-Scores
2
Which of the following is NOT a step used in calculating standard
deviation?
Subtracting the value of each data set from the mean.
Dividing the sum of each value by the total number of values plus 1.
, Calculating the mean of the data set.
Squaring the difference of x - u.
RATIONALE
Recall the standard deviation . So there is no addition of 1 to any values.
CONCEPT
Standard Deviation
3
In which of these cases should the median be used?
When the data has small variance
When the data has extreme values
When the data has nominal values
When data has no outliers
RATIONALE
Since the mean uses the actual values in the data, it is most affected by outliers and
skewness. So, we only want to use the mean when the data is symmetric as a measure
of centrality. When the data is skewed or has extreme values,
the median is a better measure since it is not as sensitive to these values.
CONCEPT
Measures of Center
4
The average daily rainfall for the past week in the town of Hope Cove is
normally distributed, with a mean rainfall of 2.1 inches and a standard
deviation of 0.2 inches.
If the distribution is normal, what percent of data lies between 1.9
inches and 2.3 inches of rainfall?
95%
,
34%
99.7%
68%
RATIONALE
Recall that if the data is normal, then the 68-95-99.7 rule applies which states that 68%
of all data points fall within one standard deviation of the mean, 95% of all data points
fall within two standard deviations of the mean, and 99.7% of all data points fall within
three standard deviations of the mean.
1.9 inches and 2.3 inches are both 0.2 inches from the mean of 2.1 inches, which is the
same as one standard deviation in either direction. This tells us that 68% of the data
should lie between 1.9 inches to 2.3 inches.
CONCEPT
68-95-99.7 Rule
5
Ralph records the time it takes for each of his classmates to run around the
track one time. As he analyzes the data on the graph, he notices very little
variation between his classmates’ times.
Which component of data analysis is Ralph observing?
The overall spread of the data
The center of the data set
An outlier in the data set
The overall shape of the data
RATIONALE
Since Ralph is looking at the variation of data, this is examining the spread of the data.
CONCEPT
Data Analysis
