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Lesson Menu 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 5-Minute Check 1 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 5-Minute Check 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?

Vocabulary statistical inference statistic parameter univariate data measures of variation mean absolute deviation standard deviation variance

Example 1 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

Example 1 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

Example 1 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?

Example 1 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?

Concept

Example 2 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 1The mean of this set of data is 16. Step 2Find 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| = or 14 Step 3Divide the sum by the number of values. 14 ÷ 6 ≈ 2.3 Answer:about 2.3

Example 2 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.

Concept

Example 3 Find the Variance and Standard Deviation Find the mean, variance, and standard deviation of 5, 7, 8, 14, 16. Step 1To find the mean, add the numbers and then divide by how many numbers are in the data set.

Example 3 Find the Variance and Standard Deviation Step 2To find the variance, square the difference between each number and the mean. Then sum the squares and divide by the number of values.

Example 3 Find the Variance and Standard Deviation Step 3The 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. Variance Take the square root of each side. Use a calculator.

Example 3 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.

Example 4 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.

Example 4 A B C D 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.

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