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

A. mode

B. median

C. range

D. mean

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?

Over Lesson 12–2

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?

Which survey question shows bias?

• 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 ordersPopulation: all movie orders for the day of the sampleSample statistic: median number of rentals per order in the samplePopulation 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 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

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 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

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?

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

A. 12

B. 7

C. 2.5

D. 2

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.

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.

Answer: The mean of the set of data is 10, the variance is 18, and the standard deviation is approximately 4.2.

VarianceTake the square root of each side.

Use a calculator.

A. 8.3; 2.9

B. 6.8; 2.6

C. 5.4; 2.3

D. 3.4; 5.8

Find the variance and standard deviation of 22, 24, 19, 18, 17.

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.

A. 194.3

B. 205.1

C. 168.1

D. 167.3

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.