Statistics Exam 3
Number of children in household Frequency 0 - 5 1 - 9 2 - 9 3 - 7 4 - 0 5 - 1 What is the mean number of children in each household?
1.7
One common system for computing a grade point average (GPA) assigns 4 points to an A, 3 points to a B, 2 points to a C, 1 point to a D, and 0 points to an F. What is the GPA of a student who gets an A in a 2-credit course, a B in each of three 3-credit courses, a C in a 2-credit course, and a D in a 3-credit course? The mean grade point score is__________?
2.6
A student earned grades of C, A, B, and A. Those courses had these corresponding numbers of credit hours: 4, 3, 1, and 3. The grading system assigns quality points to letter grades as follows: A=4, B=3, C=2, D=1, and F=0. Compute the grade point average (GPA) and round the result to two decimal places.
3.18
Speed (miles per hour) Frequency 42-45 -23 46-49 - 16 50-53 - 7 54-57 - 4 58-61 - 1 What is the mean of the data?
47.1
Empirical rule
68% within 1 SD 95% within 2 SD 99.7% within 3 SD
What percentages are associated with the Empirical Rule?
68%, 95%, 99.7%
Range rule of thumb/significant
95% lands within 2 standard deviations from the mean
A student earned grades of 66, 77, 88, and 95 on her four regular tests. She earned a grade of 70 on the final exam and 70 on her class projects. Her combined homework grade was 85. The four regular tests count for 40% of the final grade, the final exam counts for 30%, the projects count for 10% and homework counts for 20%. What is her weighted mean grade?
=77.6
How to find Mean
dividing the sum of all values in a data set by the number of values
How to find Midrange
Add together the maximum and minimum data value and divide by two.
Mean
Add up all the values and divide by the number of values
he body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.18°F and a standard deviation of 0.54°F. Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of healthy adults with body temperatures within 2 standard deviations of the mean, or between 97.10°F and 99.26°F? b. What is the approximate percentage of healthy adults with body temperatures between 97.64°F and 98.72°F?
Approximately 9595% of healthy adults in this group have body temperatures within 2 standard deviations of the mean, or between 97.10°F and 99.26°F. (Type an integer or a decimal. Do not round.) Part 2 b. Approximately 6868% of healthy adults in this group have body temperatures between 97.64°F and 98.72°F. (Type an integer or a decimal. Do not round.)
Weighted Mean
Calculating gpa's
normally distributed
Every value is spread out
A student's course grade is based on one midterm that counts as 10% of his final grade, one class project that counts as 15% of his final grade, a set of homework assignments that counts as 45% of his final grade, and a final exam that counts as 30% of his final grade. His midterm score is 81, his project score is 97, his homework score is 75, and his final exam score is 66. What is his overall final score? What letter grade did he earn (A, B, C, D, or F)? Assume that a mean of 90 or above is an A, a mean of at least 80 but less than 90 is a B, and so on.
Final Score 76.1 Letter Grade is a C
How to find Mode
Find the number that appears the most often.
Use the empirical rule to solve the problem. At one college, GPA's are normally distributed with a mean of 2.38 and a standard deviation of 0.47. Between what two values do approximately 68% of the GPA's lie?
Lower bound = 1.911.91 Upper bound = 2.85
Mean of Frequency Distribution
Make a table with midpoints and f*x
Midrange
Maximum data + Minimum data divided by 2
Median
Middle number (least to greatest)
Outliers
Numbers that are much greater or much less than the other numbers in the set
the less standard deviation
closer to the mean
Listed below are the amounts (dollars) it costs for marriage proposal packages at different baseball stadiums. Find the range, variance, and standard deviation for the given sample data. Include appropriate units in the results. Are there any outliers, and are they likely to have much of an effect on the measures of variation? 40 50 50 55 70 95 95 100 195 212 270 375 500 2000 2750
Range of sample data= 2710 Dollars Standard Deviation of Sample data= 802.5. Dollars Variance of Sample data= 644071.8 Dollars Squared
Range
Take maximum value minus the minimum value
Distribution is symmetrical
The higher values look like a pyramid in the middle of the graph
Distribution is skewed to the right
The higher values will be on the left side
Distribution is skewed to the left
The higher values will be on the right side
Mode
The number that shows up the most
to find the percentile
count up to the number then divide by numbers (ex. 44/50
How to find midpoints
add and divide by 2
significantly high values
add the standard deviation twice to the mean
How to find Median
arrange numbers from least to greatest and find the middle value and if there are two add the two numbers together and divide by 2.
the greater the standard deviation
farther from the mean
how to calculate z score
given value is first on top, mean goes second on top, then subtract top number then divide by standard deviation
If standard deviation for set data is 0 then all values will be
identical
z scores
measure the distance of a score from the mean in units of standard deviation
Sample
specific group that you will collect data from
Variance
standard deviation squared
significantly low values
subtract standard deviation twice from the mean
Population
the entire group that you want to draw conclusions about
Midpoints
the point halfway between the endpoints (ex. 40+44 then divide by 2)
When data value are less than the mean
the z score is negative
n represents
total number of values added up
data value is considered signifigantly low or high when
z score is -2 or greater than 2
