Transcript Over Lesson 12–2 - Auburn School District

Five-Minute Check (over Lesson 12–2)
Then/Now
New Vocabulary
Example 1: Identify Statistics and Parameters
Concept Summary: Measures of Variation
Key Concept: Mean Absolute Deviation
Example 2: Use the Mean Absolute Deviation
Key Concept: Variance and Standard Deviation
Example 3: Find the Variance and Standard Deviation
Example 4: Real-World Example: Statistical Analysis
Over Lesson 12–2
An amusement park records the number of visitors
to an old attraction they are considering removing
over 10 days. The results are shown in the table.
Which measure of central tendency best represents
the data?
A. mode
B. median
C. range
D. mean
Over Lesson 12–2
Which survey question shows bias?
A. What would you do with a
million dollars?
B. Which country record should
win album of the year?
C. Where would you travel if you
won a trip outside the U.S.?
D. Who will you vote for in the
next election?
• statistical inference
• statistic
• parameter
• univariate data
• measures of variation
• mean absolute deviation
• standard deviation
• variance
Identify Statistics and Parameters
A. Identify the sample and the population for the
situation. Then describe the sample statistic and the
population parameter.
A movie rental business selects a random sample of 50
orders in one day. The median number of rentals per
order is calculated.
Answer:
Sample:
50 movie orders
Population:
all movie orders for the day of the
sample
Sample statistic:
median number of rentals per order
in the sample
Population parameter: median number of rentals per order
for all rentals the day of the sample
Identify Statistics and Parameters
B. Identify the sample and the population for the
situation. Then describe the sample statistic and the
population parameter.
A stratified random sample of 2 trees of each species is
selected from all trees at a nursery. The mean height of
trees in the sample is calculated.
Answer:
Sample:
2 trees of each species found
at the nursery
Population:
all trees at the nursery
Sample statistic:
mean height of trees in the
sample
Population parameter:
mean height of all trees at the
nursery
A. The coach of a basketball team measures the
height of his starting team’s vertical jumps. He then
calculates the average of their highest jump. What
is the population parameter of this survey?
A. the average vertical jump of
the starting team
B. the starting team
C. the average vertical jump of
the entire basketball team
D. the entire basketball team
B. The principal of a new school decided to conduct a
survey to determine if the student population enjoyed the
new school mascot. He asked every student who entered
school in the side door to rate the mascot on a scale of
1 to 10, and then averaged the scores. What is the sample
statistic of this survey?
A. the average score the mascot receives
from students entering the side door
B. the average score the mascot receives
from the whole student population
C. all the students who entered the side
door
D. the entire student population
Use the Mean Absolute Deviation
PETS A rescue agency records the number of pets
adopted each month: 14, 18, 12, 17, 15, 20. Find the
mean absolute deviation.
Step 1
The mean of this set of data is 16.
Step 2
Find the sum of the absolute value of the
difference between each value in the data
set and the mean.
|14 – 16| + |18 – 16| +|12 – 16| + |17 – 16| +
|15 – 16| + |20 – 16| = 2 + 2 + 4 + 1 + 1 + 4
or 14
Step 3
Divide the sum by the number of values.
14 ÷ 6 ≈ 2.3
Answer: about 2.3
FISHING Giles and his father record the number of
catfish they catch each month out of the river
behind their house: 6, 8, 10, 4, 5, 9. Find the mean
absolute deviation.
A. 12
B. 7
C. 2.5
D. 2
Find the Variance and Standard Deviation
Find the mean, variance, and standard deviation of
5, 7, 8, 14, 16.
Step 1
To find the mean, add the numbers and then
divide by how many numbers are in the data
set.
Find the Variance and Standard Deviation
Step 2
To find the variance, square the difference
between each number and the mean. Then
sum the squares and divide by the number of
values.
Find the Variance and Standard Deviation
Step 3
The standard deviation is the square root of
the variance.
Variance
Take the square root of each
side.
Use a calculator.
Answer: The mean of the set of data is 10, the variance
is 18, and the standard deviation is
approximately 4.2.
Find the variance and standard deviation of 22, 24,
19, 18, 17.
A. 8.3; 2.9
B. 6.8; 2.6
C. 5.4; 2.3
D. 3.4; 5.8
Statistical Analysis
TEXT MESSAGES Daisy kept track of the number of
text messages she sent each month for 6 months.
Find the standard deviation of the data set.
Answer: So, the standard deviation is about 84.1.
The city of Hardesty keeps track of the number of
fans the local baseball team draws to the games
each month. Find the standard deviation of the data
set.
A. 194.3
B. 205.1
C. 168.1
D. 167.3