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Example Questions
Example Question #1 : How To Find The Standard Deviation Of The Sum Of Independent Random Variables
A high school calculus exam is administered to a group of students. Upon grading the exam, it was found that the mean score was 95 with a standard deviation of 12. If one student's z score is 1.10, what is the score that she received on her test?
108.2
110.1
105.3
109.2
107.2
108.2
The z-score equation is given as: z = (X - μ) / σ, where X is the value of the element, μ is the mean of the population, and σ is the standard deviation. To solve for the student's test score (X):
X = ( z * σ) + 95 = ( 1.10 * 12) + 95 = 108.2.
Example Question #133 : Statistical Patterns And Random Phenomena
First, find that 
Then find the mean and standard deviation of 
Example Question #134 : Statistical Patterns And Random Phenomena
Consider the discrete random variable 
-
with
-
with
-
with
-
with
Compute the variance of the distribution.
The variance of a discrete random variable is computed as
for all the values of 
First, we compute 
So we have
Example Question #131 : Statistical Patterns And Random Phenomena
Clothes 4 Kids uses standard boxes to ship their clothing orders and the mean weight of the clothing packed in the boxes is 
Note that the weight of a packed box = weight of books + weight of box + weight of packing material used.
It is given that 
The calculation of the standard deviation of the weights of the packed boxes is
Example Question #1 : How To Find The Median For A Set Of Data
Six homes are for sale and have the following dollar values in thousands of dollars:
535
155
305
720
315
214
What is the median value of the six homes?
The median is determined by ordering the values in the group from least to greatest: 155, 214, 305, 315, 535, 720. The value directly in the middle is the median. For instance, if there are five numbers, the third is the median. Here, we have an even number of values so there is no value directly in the middle. To find the median when there is no middle-most value, find the average of the two middle values. The mean is determined by adding the two values and dividing by two (the number in the group):
Example Question #1 : How To Find The Median For A Set Of Data
Find the median of the set.
The median is the middle value of the set in increasing order.
In this set of 11 entries, the median is the 6th entry of the set in increasing order, or 6.
Example Question #2 : How To Find The Median For A Set Of Data
Find the median of the set
The median is the middle value of the set in increasing order.
In this set of 6 (or any even number of) entries, the median is the mean of the two middle entries of the set in increasing order
or
Example Question #201 : Ap Statistics
Let 
Find the median of the set.
The median is the middle value of the set in increasing order.
In this set of 8 (or any even number) entries, the median is the mean of the two middle entries of the set in increasing order
or
Example Question #1 : Data
Suppose a basketball team plays six games and scores the following points: 69, 78, 82, 69, 98, 85. Find the median.
69
80
75.5
82
80
To find the median of a sample with an even sample size, order the values from smallest to largest, take the two values in the middle, add them, and divide that by zero.
69, 78, 82, 69, 98, 85
69, 69, {78, 82} 85, 98
(78+82) / 2 = 80
Example Question #1 : Univariate Data
A sample consists of the following observations:
The mean is
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