Question

please answer 1) and 2)

PART THREE Below are the times for running a mile for 61 runners (measured in seconds). Use the 1-Var Stats calculator results shown to answer question # 1 and #2. L2 Descending order IL2 L3 1 L1 IL3 IL2 1 L1 L3 L1 433 429 420 420 417 4i6 416 599 584 S80 579 577 571 569 566 561 439 436 --- 522 L1(21) 416 L1(7) 572 L1C14)436 L3 1 L2 1 L1 IL3 L2 1 L1 L1 L3 L2 371 369 365 367 366 36 364 404 403 379 379 377 414 412 412 405 L1C42)=364 L1C28) 406 L1C35)373 1 L1 L2 L3 L1 1 L1 L2 IL3 1 L2 L3 360 360 345 341 340 322 320 319 315 310 300 R50 R22 L1C49)350 1-Var Stats X=414.1967213 Ex-25266 Ex2=10921470 Sx 87.2138788 ox -86.49605689 In 61 L1C56) 322 1-Var Stats fn 61 minx=300 Q1 357.5 Med=379 Q3=431 maxx-599 L1C57) 320 1) Assuming the runner's times a symmetric bell shaped distribution, Empirical Rule to answer parts a-d (rounded to two decimal places). use the a) 68% of the running times are between what values? b) What percent of the running times are at least two deviations below the mean? c) Running times of at least two deviations from the mean are considered unusual. How many seconds is the unusual time cutoff? d) How many runners are considered unusual? 2) a) What is the IQR of the running times? b) What are the inner fences of the running times? c) What are the outer fences of the running times? d)Potential outliers would fall between what running times? e) What is the percentile rank of a runner with a running time of 360? Give a non-statistical interpretation of part "e" (i.e. what does this number represent in simple English terms?). g) What is the value of Ds? PART FOUR 2pcy PING PONG BALLS

Answer 1

1. a) 68% of the values are between the first and third quartiles i.e. between 357.5 and 431

b) Here mean =414.1967, SD=86.4961 so that the cut off for two deviations from mean is

mean-2SD=414.1967-2*86.4961=241.2045.

We find the Z score for the least observation 300 as (300-414.1967)/86.4961= -1.320253. Hence no observations are below 241.2045 (i.e. corresponds to a Z score of -2 or below) and the required percentage is 0%.

c) The cut off is mean+2SD=414.1967+2*86.4961= 587.1889 as no observations lie below mean-2SD=414.1967-2*86.4961=241.2045.

d) The number of runners having time more than 587.1889 is one (I.e. 599). i.e.

2. a) IQR=Q3-Q1=431-357.5=73.5

b) Inner fences: Q1-1.5*IQR=247.25 , Q3+1.5*IQR=467.75

c) Outer fences: Q1-3*IQR=137 , Q3+3*IQR=578

d) Observations falling outside the interval (Q1-1.5*IQR, Q3+1.5*IQR) =(247.25,467.75) are potential outliers.

Observations falling outside the interval (Q1-3*IQR, Q3+3*IQR) =(137, 578) are extreme outliers.

e) There are 15 observations below the value 360. Then percentile rank of the observation 360 is 100*15/61%=24.59%.

f) The percentile rank of 24.59% indicates that 24.59% of the running times are less than 360.

g) D5 is the fifth decile or median, which is 379.