a. For each breed group of bulls listed, calculate the mean, median, and mode. b

Question

a. For each breed group of bulls listed, calculate the mean, median, and mode.

b. For each breed group of bulls listed, calculate the range, sample variance, and the sample standard deviation for PAP scores.

c. Based on these samples, which breed would you expect to have a lower incidence of PAP? Why?

d. Which breed has more variance in bull PAP scores?

e. Do the distribution of scores for each breed appear to follow the Empirical Rule? Why or why not?

f. Now, combine both breeds and calculate the mean, median, sample variance and sample standard deviation from the combined PAP scores.

Ive got a-d done, I just dont understand how to do e and explaining why/why not. G would also be helpful to explain.

Hereford (Test no., Name, PAP score: Durango Sheyenne 45 Top Shelf Redeem Tested All American 39 Resource 39 Bluestem 35 7HP105 7HP107 7HP108 7HP109 7HP110 7HP111 7HP112 7HH57 39 38 38 39 Simmental (Test no., Name, PAP Score): 7SM60 7SM61 7SM66 7SM67 7SM68 7SM74 7SM75 7SM76 7SM78 7SM79 7SM80 7SM82 Yukon Rimock 34 Vegas Convoy 44 Husker Stellar Robust Rancher Everclea 42 Optimizer 43 Wide Range 36 Broadway44 36 40. 42 40. 39 39

Explanation / Answer

Solution for (e) and (f) only as desired

[Ive got a-d done, I just dont understand how to do e and explaining why/why not. G would also be helpful to explain.]

Question does not have part (G). Taking this as a typo in stead of (f), (f) is solved.

Part (e)

The Empirical Rule also known as 68 – 95 – 99.7 percent rule:

P{( µ - ) X ( µ + )} = 0.68; i.e., 68% of observations lie within ± 1SD from mean

P{( µ - 2) X ( µ + 2)} = 0.95; i.e., 95% of observations lie within ± 2SD from mean

P{( µ - 3) X ( µ + 3)} = 0.997 i.e., 99.7% of observations lie within ± 3SD from mean.

Now, to work out the solution,

Using Excel , the mean (Xbar), variance (S2) and standard deviation (S) of PAP scores are found to be as follows:

Group

n

Xbar

S2

S

Xbar

± 1S

Xbar

± 2S

Xbar

± 3S

1

8

39.00

6.75

2.60

2

12

39.92

11.74

3.42

Breed

n

Xbar

S2

S

Xbar ± 1S

Xbar ± 2S

Xbar ± 3S

1

8

39.00

6.75

2.60

36.40 – 41.60

33.80 – 44.20

31.20 – 46.80

2

12

39.92

11.74

3.42

36.5 – 43.34

33.08 – 46.76

29.66 – 50.18

Percentage of observations within Empirical Rule

Breed

Xbar ± 1S

Xbar ± 2S

Xbar ± 3S

1

75.0

87.5

100

2

58.3

100

100

Part (f)

Sample Measures for Combined PAP Scores

N = 20.

Mean = 39.55 Answer 1

Variance = 9.95 Answer 2

SD = 3.15 Answer 3

Median = (39 + 39)/2 = 39 Answer 4

Group

n

Xbar

S2

S

Xbar

± 1S

Xbar

± 2S

Xbar

± 3S

1

8

39.00

6.75

2.60

2

12

39.92

11.74

3.42

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