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# Section 1-3

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Measures of Center

Measures of Center

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### Transcript

• 1. Section I-5 e Measures 0? Center
• 2. I n-Class Activitg (P. 19) «an Wtng’? So we can analgze data in various wags «av How do gou enter data’? a How do gou ﬁnd characteristics ot the data’?
• 3. Mean: Just another word tor the average; add it all up, then divide b3 the total number . Median: The middle value ot a data set when Put in order It there is an even number ot values, gou have to tal<e the average oi: the two middle terms Mode: The value that shows up the most Hint: The m“O”de shows up the m“O”st Sigma (2): It’s a Greelc letter (we’ll see lots ot these this year). We use this letter tor “summation”
• 4. . . . - . ~.-, .‘. . - -— ' "-‘r — . .t. ... .. _, -- -. _5.. ., -. ,_ _, , _ , .. _ . ..‘ -. _:, .-- » »»« _ . . . ._¢ . _._. .-_ Summation Notation 10 i‘= llndex The sum ot the lirst ten terms is g, - uv 7 Index: Tells us where on the list the value is Y i i 0 % 9 E. ‘tj T S 9 : ' T Es f f. 1 _. \$ 1‘ E l 2 2 i
• 5. J l Eixample ~ 3 _ notation tor each set ot data. Reter to the table on Page ZO, dealing with the ages ot actors and actresses when theg won the Oscar 3 tor Best Actor/ Actress. Write the summation 25 25 Men= Zm, ~ = 1134 womcnzzwi = 1012 i= l i= l . . _ ~ i , ... ,-. ..a. ._. r- ~y~v—- ~ 1 -. .. «Oi ‘ - . .-n. —— -. ‘. r¢_r . . . »p F4‘ -’1‘mI’V~““pm . -o-4- ov-9 . ‘V ’ '** ”""‘ _ . “
• 6. A statistical wag ot delining the mean:
• 7. Example 2. Consider the set {x}, x2, x3, x4, x5, x6, x7, X3} a. Represent the sum ot the elements in the set in 226;’ i=1 - i 3 S summation notation. 8 V What expression represents the mean ot the elements ot the set? 3 Xzgxi v-4 . _. - 1 , . .0’ ‘ . _, . . up-9-0 . — - - . '~on\$-o. ~4-u. -0.»-A»? -19- , ... .s. .-. ... .»—. V.. -V. .~. ~. -y. -.. »v-»-4---o-—»-_ *" “"' i - " I’ _ -
• 8. fi'f*3‘-? :'? %?k‘~¥5? 9?. .71‘-'3-)3‘ 7 ‘ T From the given intormation, can the median oi: the ' . " lset be determined? Alt not, explain whg it cannot be W determined. Do we l<now the actual values? No Then how can we put them in order? We can’t!
• 9. Example 5 Find the median age oi: the women winning - Wimbledon singles championships trom 1970 to 1990. 1 999 2 11207898656789 5 H05 27
• 10. Example 4 l « 3 l ’ _ ot plagers on the varsity team at Matt Mitarnowsl<i 3 Memorial High School. 8? . i 9 Number 0t 5 5 2_ 2_ plauers Lmww —--o, ..9v. .-8-. ~.. »-. g_4g. .-‘ 1 The chart below gives intormation about the heights E ~_-. ,_, _ . ,_Q. ... n. -.. —.. .- ~ 4- - V-*
• 11. ‘ if a. How mang members are on the team’? L V‘ V Find the mean height. *3 V 8' c. Find the median height. . . . _, . . .,. ~. __, _, "-5-—-7 --' 7- -' 1 -' - -->: -."'. ‘ -__. -. __. .:— ~ *»« -_ ' : - . -. There are 15 members on the team 13 3-6 = xi = L23 = 71 inches 13 13 70 inches
• 12. dv~. ..-—. ... -.. m.. .—q-Aouun-no--v~&~r . d. Which number, the mean or median, best describes the tgpical height ot a member ot the ‘ team? Whg? The median better describes the team, as there is a high number (an outlier. ..79) ,9 1 which mal<es the average higher. -1 *1 - 1 1 . .5 pp. was-. .-4-u-. -o. —auQ_4‘. -‘ 1 1 t I t i l l l 0 I in S I C i
• 13. Example 5 A class has 20 students. Let g, - = the test grade ot - the it“ student. a. Use summation notation to express the total ot the test grades tor the class. 20 _/ _F.8i ' 1 I:
• 14. AL b. What does . ./fl‘. gi represent’? 20 The mean ot the test scores tor the class.
• 15. 1’, ‘no , ;-ﬁr . 4i" 5 . . , _,-u