Assignment N0. 1MATH - 505 Business Maths & Stats(MBA 2K14 A & B)PROBLEM 1:a.) A storeowner kept a tally of the sizes of suits purchased in her store. Which measure of central tendency should the storeowner use to describe the average size suit sold?ANSWER: MODEb.) A tally was made of the number of times each color of crayon was used by a kindergarten class. Which measure of central tendency should the teacher use to determine which color is the favorite color of her class?ANSWER: MODE, BECAUSE REPETION OF COLOR WILL BE THE MOST FAVIOURITE COLOR BY CLASS.c.) The science test grades are posted. The class did very well. All students taking the test scored over 75. Unfortunately, 4 students were absent for the test and the computer listed their scores as 0 until the test is taken. Assuming that no score repeated more times than the 0's, what measure of central tendency would most likely give the best representation of this data?ANSWER: 75, 76, 77, 78, 79 I WILL USE MEDIAN BECAUSE MEDIAN TELLS US THE MOST CENTRAL VALUE OF DATA. PROBLEM 2:There are three different basketball teams and each has played five games. You have each team's score from each of its games.Game 1Game 2Game 3Game 4Game 5

Jaguars6787549978

Wolves8590448046

Lions32101658855

ANSWER: JAGUARS 54, 67, 78, 87, 99 WOLVES 44, 46, 80, 85, 90 LIONS 32, 55, 65, 88, 101A.M = Sum of all values / no of values MEAN OF JAGUARS = 77, MEAN OF WOLVES = 69, MEAN OF LIONS = 68.21.) Suppose you want to join one of the three basketball teams. You want to join the one that is doing the best so far. If you rank each team by their mean scores, which team would you join?ANSWER: I WILL CHOOSE JAGUARS BECAUSE OF HIGHER SCORE.2.) Instead of using mean scores, you use the median score of each team to make your decision. Which team do you join?ANSWER:JAGUARS 54, 67, 78, 87, 99 WOLVES 44, 46, 80, 85, 90 LIONS 32, 55, 65, 88, 101MEDIAN IS THE MOST CENTRA VALUE. FOR UNGROUP DATA, WE WILL USE FORMULA AS MENTION BELOW, MEDIAN= (n+1)/2 th item, Calculations as followsMEDIAN OF JAGUARS = (5+1)/2 th item = 3th item = 78MEDIAN OF WOLVES = (5+1)/2 th item = 3th item = 80MEDIAN OF JAGUARS = (5+1)/2 th item = 3th item = 65RESULT: I WILL CHOOSE WOLVES BECAUSE OF HIGHER SCORE.3.) Pretend you are the coach of the Lions and you were being interviewed about your team for the local newspaper. Would it be better for you to report your mean score or your median score?ANSWER: WE USE MEASURE OF CENTRAL TEDENCY ACCORDING TO SITUATION.THE MEDIAN IS THE MOST CENTRAL VALUE WHILE MEAN IS ALWAYS AVG VALUE OF DATA (DATA IN SYMMMETRIC FORM). IN THIS,THE MOST CENTRAL VALUE (MEDIAN) IS GREATER THEN AVG (MEAN), SO I WILL USE MEDIAN SCORE. PROBLEM 3:You have four 10 km segments to your automobile trip. You drive your car: 100 km/hr for the first 10 km 110 km/hr for the second 10 km 90 km/hr for the third 10 km 120 km/hr for the fourth 10 km. What is harmonic mean speed?ANSWER: 1ST 10 KM2ND 10 KM3RD 10 KM 4RTH 10 KM 1OO KM/H110 KM/H9O KM/H12O KM/HDATA IS UNGROUP SO WE WILL USE BELOW MENTIONN FORMULA FO SOLUTION H.M = n / (1/n) = 4 / (1/100 + 1/110 + 1/90 + 1/120)= 4/0.03853= 103.81 PROBLEM 4:Given the following frequency distributionof firstyear students of a particular college. Calculate the Harmonic Mean.Age (Years)1314151617

Numberof Students251373

ANSWER: DATA IS in GROUP FORM SO WE WILL USE ABOVE MENTIONN FORMULA FO SOLUTION H.M = f / (f / n)= 2+5+13+7+3 / (2 / 13 + 5/ 14 + 13/15 + 7 /16 + 3/17)= 30 / 1.99= 15.15PROBLEM 5:Your investment earns 20% during the first year, but then realizes a loss of 10% in year 2, and another 10% in year 3. a) Calculate the arithmetic mean for the average rate of return?ANSWER: A.M = Sum of all values / No of values= 20 % + (- 10%) + (- 10%) / 4 = 0b) Calculate the geometric mean rate of return?ANSWER: FOR G.M RATE OF RETURN, FOLLOWING FORMULA WILL BE USED FOR CALCULATION, 1+ R (G) = R (G) = - 1 = - 1 = - 1 = - 1 = 0.9905 1 = - 0.009421 = 0.9421 (-VE SIGN IS SHOWING LOSS) c) Which of the two averages is accurate?ANSWER: WE WILL USE G.M (Rate of Return) BECAUSE THIS IS SHOWING THE TRUE PICTURE OF DATA.PROBLEM 6:Sales data for drug X for a small drug manufacturer is shown below.Year20022003200420052006

Cases1250013250143101574117630

a) Calculate the percent increase from the previous in sales for years 2003, 2004, 2005 and 2006

ANSWER:

FOR 2003, FOR 2003 = VALUE OF 2003 VALUE OF 2002 / VALUE OF 2002FOR 2003 = 13250 12500 /12500FOR 2003 = 0.06FOR 2003 = 6 %

FOR 2004, FOR 2004 = VALUE OF 2004 VALUE OF 2003 / VALUE OF 2003FOR 2004 = 14310 13250 /13250FOR 2004 = 0.08FOR 2004 = 8 %

FOR 2005, FOR 2005 = VALUE OF 2005 VALUE OF 2004 / VALUE OF 2004FOR 2005 = 15741 14310 /14310FOR 2005 = 0.10FOR 2005 = 10 %

FOR 2006, FOR 2006 = VALUE OF 2006 VALUE OF 2005 / VALUE OF 2005FOR 2006 = 17630 15741 /15741FOR 2006 = 0.12FOR 2006 = 12 %

b) Using the percentage numbers from above, calculate the arithmetic average percentage increase.

ANSWER:

A.M = 6% + 8% + 10% + 12% / 4 A.M = 9%

c) Calculate the geometric mean rate of increase using numbers in a)

ANSWER: G.M = Antilog [ log x / n]

FOR 2003 = Log 6 = 0.7781FOR 2004 = Log 8 = 0.9030FOR 2005 = Log 10 = 1 FOR 2006 = Log 12 = 1.0791

G.M = Antilog [ (0.7771 + 0.9030 + 1 + 1.0791 / 4]G.M = Antilog (0.9400)G.M = 8.71%

d) Project sales for the year 2009 using the geometric mean rate of increase calculated in c)

ANSWER:

FOR 2006 = 17630

FOR 2007 = 17630 * 8.711% = 1535.74FOR 2007 = 17630 + 1535.74 = 19165.74FOR 2007 = 19165.74

FOR 2008 = 19165.74 * 8.711% = 1669.33FOR 2008 = 19165.74 + 1669.33 = 20835.07FOR 2008 = 20835.07

FOR 2009 = 20835.07* 8.711% = 1814.94FOR 2009 = 20835.07+ 1814.94 = 22650.01FOR 2009 = 22650.01