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Practice Questions Mean, Median, and Mode 1. Find the mean, median, and mode for each set of data. Round your answer to the nearest tenth where necessary. a) 8, 10, 23, 10, 14, 16, 19-7 = 8 / 3 2,5 b) 6, 3, 8, 6, 17, 8 fte 8 int_pliti. 3 4, 4. y2 /7 t- 2- rito de_ 67 8 c) 9, 13, 7, 2, 18 nt.tet,) '921 8 fra-ire,,,.2 7 /3 /8 huocit. /10/2e, d) 3, 4, 6, 6, 10, 16 LLS/4 = 2 (c, V. 2. Mark receives the following marks on four mathematics tests: 78, 75, 82, 74 What is the lowest mark that Mark can receive on his fifth test in order for the mean of his test marks to be at least 80? l esa 54i Pktittif AC- j 2.1 fit tri2fi.da 4 A c r heal 4 aiyef 7c-r 12-6 c7(le 33 5 910-6 5) 7,-niefrif efri VAL -1-ctsiL
3. Which of the three measures of central tendency is most suitable to describe the following sets of data? a) The typical annual rainfall in Brandon b) The most common size of T-shirt sold at a fundraiser - c) The usual number of pages in a particular magazine 3 2-yrt" o c d) The average mark of a student in a course ct no ' r, 4. Eva has a mean mark of 50% on her first three math tests. She receives a mark of 70% on her fourth test. Since the mean of 50 and 70 is 60, Eva states that her new mean mark in math is 60. Is her reasoning correct? Explain. /0 111-70 s t4-8. Z- 4 9 tj t 0 `61 ka_ virery c. 5. If a random sample of 50 people produces a mean income of $36,000, would a random sample of 100 people produce a mean income of $72,000? Explain. c514. N t, / Q4 7 hart ale( et, VI' c, '4'- 9/ T A 0 d IL J (is a d Jf sariz
6. In one month, Ian buys two lunches at $10.95 each, five lunches at $11.75 each, and one lunch at $12.25. Find the mean, median, and mode for the amount that Ian spends per lunch during the month. ntean ( 2 X /6,9C) e (cyji,7s- _j ( I z. 12,2-0 iw-ctc:1--- /4K /0,13"-- it 7C Fyi -t a, 7C 7. A sales department is made up of three divisions. The annual salary for each employee of a division is the same and is indicated in the following table. re -.S7'; - '''...,,,, c;._,. 44,- _......n.,. Ai. Erdp.,. o _.e -e... _._, :EatEit 3 $52,000. _. ;:eentra.1.. 7WeOteiiit a) Explain why the mean annual income of all the employees cannot be found by adding the numbers in the third column and dividing by three. 1/071L /14.442 C:Lib el 4) In-LQ--r b) Find the mean annual income of all the employees. C 3 y 2_0 6 c_ ( 2 s-- 3-1/47e6 0) Cs- A, 2,E 506 33 3* ik 727,22-3 -
Practice Questions Outliers and their effect on data 1. Find the outliers for the following data sets. State the new data sets after removing these outliers. a) r598, 10, 13, 7, g i /01 /3 ( 1 / 5 b) 12, 14, 16, 15, 14, 13, 11, 23 tnie--7 rza Lsz_ 717- rz,291171- - 2. A billionaire is in a room with 10 Roofmart workers. Assume the billionaire's yearly income is $40,000,000. Assume that the 10 Roofmart workers each earn a yearly income of approximately $30,000. a) What is the mean income of all the people in the room? Vo 400 coo ( / 0 x 30 o 1 3 4 3 434, 3 b) Is the billionaire's income classified as an outlier? vesi How does the outlier affect the mean income? Is the mean income an accurate representation of the typical income in the room? 14/ 1--e 74.7 d) Which measure of central tendency would be the best representative of the typical income in the room? - - 4 -
3. Sheila was trying to find the trimmed mean of the following data set by removing a low score and a high score: 4,7, 3, 8, 12, 34, 23, 41, 73, 46, 14, 94, 25, 73, 25, 63, 24, 46, 52, 48. She thought the 10% trimmed mean was 618(20. a) What was Sheila's mistake? all no frfre 1,2-fr s O I 7/c- 3-9/ 7/0 77K b) What is the actual 10% trimmed mean? r 4. Consider the following set of numbers: 12, 34, 30, 16, 23, 18, 23, 28. a) Alia is trying to determine the median. She believes the median is 19.5. What mistake did Alia make when calculating the median? 2_ sv,./ 11_61- ear [ 4,4 o b) Calculate the mean, median, and mode. - 23 4._e_aatt 13e-2 1 2-3 c) What is true about the mean, median, and mode for this set of numbers? Why is this the case? ((IR ga[q Es- - " ct, to -5-
5. Consider the following statistics for an NHL hockey team. The mean salary for 37 players on a hockey team is $1,990,000. However, 65% of the players have a lower salary than the mean salary. The mode salary is $500,000 and the median salary is $950,000. The lowest salary is $420,000 and the highest salary is $7,000,000. a) If the mean, median, and mode are all measures of central tendency, why are they significantly different values? (41 / /74_ I -700,006 ha (ce "04 The $7,000,000 salary is an outlier. What effect does this have on the mean? rwo_ilts c) What statistic should this hockey team provide to the media to represent its typical salary value? Explain. 0 yid, cl-tb " La 17,4 -Ce---e-4 71-4-C1' / -6-
6. The heights of six members of a basketball team are as follows: 174 cm, 183 cm, 185 cm, 190 cm, 170 cm, 183 cm a) Calculate the mean, median, and mode of the heights. or 3 i13 170 i7v 7k3 A /cf3 MS b) If a player who is 204 cm tall joins the team, calculate the new mean, median, and mode. 14,1 /s-crel_ /O&5 t d ei " "7 170 /7/ (t5 c) Which measure of central tendency is most affected by the new data? Explain. Use the concept of outliers in your explanation. 171-21"- e. caca 11/1A-A2-4 otte-v, /at, kz,v -7
Practice Assignment Finding the Weighted Mean 1. In a high school class, the marks are weighted as follows: Test 1 = 15% Assignments = 20% Test 2 = 25% Participation = 5% Test 3 = 10% Final Exam = 25% Scotty had the following marks: Test 1-79 Assignments 52 Test 2 84 Participation 97 Test 3-73 Final Exam 8] What is Scotty's final mark? )(0,aC t - i YOJ x. pc 2,{) k 9-1 )4_ 0,6,c -k- E? of -77 tic 6/ 3-8 -
2. In a Brandon high school, chemistry is taught during the fall semester, the spring semester, and summer school. The following chart displays the percentage of students who passed the chemistry course. tiiir4111-'," iia:sf,iu Pa li -1-.1 ti, Fa11'.. l, - lllaggii.mil Iv. cillottor, - 1,,, ' eentawel :0,, e ''1 rnbril '..R:.Wit04,:FOritl. %:- Winter 80% Summer 68%. If 700 people took this course in the fall, 500 people took this course in the winter, and 100 people took this course in the summer, what percent of the students who took this course passed? (5ou )ckio t,0690() toa ILS114\e \ Ty t,60-00,0 514 - \o - 9 -
Percentile Practice Questions 1. Karl receives his first mark of the year in his law course. His teacher tells him that he scored at the 94th percentile. Should Karl be happy with this mark? 00-12-'1 (0 170 cv SILL_ tyl/i, 2. Are the following statements true or false? c-,,ti,9_ 4 cria ot-oso havi - ttli A tit \ Y-Ly, afati LA_ The higher the percentile rank of a score, the greater the percent of scores above that score. b) A mark of 75% always has a percentile rank of 75. A.1 c), J Pl ic d) F A mark of 75% sometimes has a percentile rank of 75. A mark of 75% never has a percentile rank of 75. e) A percentile rank of 0 is possible. o It is not possible to have a mark of 80% and a percentile rank of 50. g) The higher the percentile score, the better that score is compared to the other scores. h) A percentile rank of 70 indicates that 70% of the scores are above that score. 'I 0 No is the median. er j) Two equal scores have the same percentile rank. - 10 -
3. The following is a set of 48 scores arranged in order by columns achieved by students on an examination. 28 49 61 69 82 89 34 50 62 73 82 90 38 52 62 73 84 91 40 53 64 73 85 92 42 53 64 74 85 92 45 53 66 77 86 92 45 56 68 77 87 93 48 59 68 79 88 96 Determine the percentile rank for each of the following scores. Remember to round all percentiles to the next whole number. a) 73 2-9 )060/ b) 48 3 "2- Lii d) 96 im c iled - =- 1 6(
4. A total of 620 individuals take a government employment examination Lina scores 586 out of 800 marks. There are 498 individuals who score less thquf 586 out of 800, nd no one else has a score of 586. Find Lina's percentile rank. 9f 6 - (f0 z-o b) Find the percent mark Lina receives. > y/n 2S7 200 5. Shira's final mark in her Grade 12 Essential Math class is 92. Of the 30 students in her class, three other students received the same mark and 26 students have lower marks. a) Find Shira's percentile rank. 2 6 /op P JO b) How many students have a final mark higher than Shira? IA A- ketvi'vp -Inc-v-p- 161v-el- 3 91.0A-C (11/Pat - 12 -
6. Ricardo scores 85% on a recent test. However, his percentile rank on the test is 40. a) What can you conclude about the success rate of most of the other students who have written the test? b) What reasons could cause test results like this? za /76w 9 / t 6A-o. skene )c t oriac -teigei 7. A total of 4720 students write a university entrance examination. Lee achieves a score of 892 out of 1200. There are 3488 students who score lower than 892. There are 50 students, including Lee, who score 892. a) Find Lee's percentile rank. LL o 6 cs 4-( 2As In order to be considered for the university, Lee needs a percentile rank of 70 or better. Is Lee's score high enough for him to be considered for acceptance to the. university? 4-1- 1 1 A l c( ip kz.a-el6-11/1"l 11166-7 P1 - - 13 -
8. Examination results for 3000 students are analyzed and the following percentiles are calculated. P25 =48 P50=62 P75 = 78 P90 = 89 P 2 S PC p15 1 9 a) Approximately what percentage of students ave scored less than or equal to 62? b) Approximately how many students have scored less than or equal to 62? 50'io q 3uô O 3 6 6 6 I ce 0 c) Approximately how many students have scored more than 48? 3 15-- - g Ca d) What is the median mark of this examination? - 14 -
9. Todd has a final Grade 12 average of 89%. The college he wishes to attend will not consider any applicant if his or her percentile rank is below 82. Can Todd be sure the college will consider his application? Explain your answer. no e (Nit) [)d s, f- cktuk, 6,0AT Lr, ciao, n44-- 10. Sonya scores 38% on a recent test. However, her percentile rank on the test was 82. a) What can you conclude about the success rate of most of the other students who have written the test? hi OAA1 102&A s s-2 r -177 b) What could cause test results like this? h atio? 71-0 cud) - 15 -
11. Georgia is 1.6 m tall. She is taller than 56 of the students in her grade and no one is exactly the same height as she is. There are 152 students in her grade. a) What is Georgia's percentile rank? b 5 io 1,1 (S fig /66 p S1 b) What percentage of students is taller than Georgia? /6 tit AA cnir-- 12. A mother takes her child, Bert, to the doctor for a checkup. The doctor says Bert's weight is in the 85th percentile and his height is in the 35th percentile. a) How does Bert's weight compare to other children in his age range? St b) How does Bert's height compare to other children in his age range? frt. s - 16-