QUESTION 4: PERCENTILE & QUARTILES (10 MARKS)

-For the given data set below, calculate the 25th, 50thand 75thpercentile. Also provide the Five Number Summary.

10

11

11

11

12

12

13

15

16

16

16

17

18

19

19

19

24

25

25

25

QUESTION 5: MEAN MEDIAN AND MODE (10 MARKS)

-A frozen food company has a contract with Farm A, to provide peas for their processing plant. The daily supply of peas (in tons) over the past two weeks from Farm A has been as follows:

357.38

262.8

319.95

412.9

398.46

330.33

329.33

332.04

309.42

229.88

259.43

337.99

383.91

341.27

319.85

-The frozen food company also contracts with Farm B. The daily supply of peas (in tons) over the past two weeks from Farm B has been as follows:

364.32

295.18

352.92

420.14

314.39

143.87

421.43

291.21

306.03

348.88

333.81

191.99

324.79

315.25

435.26

5.1 CALCULATE THE RESPECTIVE MEAN, MEDIAN AND STANDARD DEVIATION FOR EACH OF THE FARMS. (3 MARKS)

5.2. ALSO, COMMENT AND INTERPRET ON THE CALCULATIONS PROVIDED AND WHAT THESE VALUES SHOW FOR EACH FARM. (3 MARKS)

5.3. WHICH FARM WOULD YOU PREFER WORKING WITH IF YOU WERE THE FROZEN FOOD COMPANY AND WHY? (4 MARKS)

QUESTION 6: THEORY (10 MARKS)

6.1. EXPLAIN THE DIFFERENCE BETWEEN A POPULATION AND A SAMPLE AND GIVE AN EXAMPLE OF EACH (2 MARKS)

6.2. EXPLAIN THE DIFFERENCE BETWEEN A PARAMETER AND A STATISTIC AND GIVE AN EXAMPLE OF EACH (2 MARKS)

6.3. DISCUSS THE REASONS FOR WHY WE MAKE USE OF SAMPLING DATA (3 MARKS)

6.4. DISCUSS TWO CHARACTERISTICS OF THE NORMAL DISTRIBUTION (3 MARKS)

QUESTION 8: CORRELATION (5 MARKS)

8.1. DISCUSS THE DEFINITION OF CORRELATION AND WHAT INFORMATION THE CORRELATION CALCULATION PROVIDES (3 MARKS)

8.2. DISCUSS THE LIMITS OF CORRELATION (TIP: BETWEEN WHAT VALUES CAN THE CORRELATION BE) (2 MARKS)

QUESTION 10: NORMAL DISTRIBUTION (15 MARKS)

The heights of adult females are normally distributed with mean 160cm and Standard Deviation 8cm.

10.1. EXPLAIN THE NORMAL DISTRIBUTION AND STANDARD NORMAL DISTRIBUTION IN YOUR OWN WORDS (4 MARKS)

10.2. FIND THE PROBABILITY THAT A RANDOMLY SELECTED ADULT FEMALE HAS A HEIGHT GREATER THAN 170CM (3 MARKS)

10.3. FIND THE PROBABILITY THAT A RANDOMLY SELECTED ADULT FEMALE HAS A HEIGHT GREATER THAN 180CM (3 MARKS)

10.4. HALF OF TALL ADULT FEMALES HAVE A HEIGHT GREATER THANHCM. FIND THE VALUE OFH.(5 MARKS)