Each of 16 students measured the circumference of a tennis ball by four differen

Question

Each of 16 students measured the circumference of a tennis ball by four different methods, which were: A: Estimate the circumference by eye B: Measure the diameter with a ruler, then compute the circumference C: Measure the circumference with ruler and string D: Measure the circumference by rolling the ball along a ruler The results (in cm) are given below, in increasing order for each method: A: 18.0, 18.0, 18.0, 21.0, 22.0, 22.0, 22.5, 22.9, 24.0, 24.0, 25.0, 25.0, 25.0, 25.0, 26.0, 26.4

B: 18.8, 18.9, 18.9, 19.7, 20.1, 20.4, 20.4, 20.4, 20.5, 20.5, 21.2, 21.6, 22.0, 22.0, 22.0, 23.6

C: 20.2, 20.5, 20.5, 20.6, 20.8, 20.9, 21.0, 21.0, 21.0, 21.0, 21.0, 21.4, 21.5, 21.5, 21.5, 21.6

D: 20.0, 20.0, 20.0, 20.2, 20.2, 20.5, 20.5, 20.7, 20.7, 20.7, 21.0, 21.4, 21.5, 21.6, 22.1, 22.3

Compute the median measurement for each method. Round the answers to one decimal place.

Method A:  cm

Method B:  cm

Method C:  cm

Method D:  cm

Compute the 20% trimmed mean measurement for each method. Round the answers to two decimal places.

Method A:  cm

Method B:  cm

Method C:  cm

Method D:  cm

Compute the first and third quartiles for each method. Round the answers to two decimal places.

Method A: First quartile   cm, Third quartile   cm

Method B: First quartile   cm, Third quartile   cm

Method C: First quartile   cm, Third quartile   cm

Method D: First quartile   cm, Third quartile   cm

Compute the standard deviation of the measurements for each method.

Method A:  cm

Method B:  cm

Method C:  cm

Method D:  cm

Explanation / Answer

Medians

A -> (24 + 22.9 )/2 = 23.45

B -> 20.45

C -> 21

D -> 20.7

For 20% trimmed mean we have to remove the largest 20% and smallest 20% of the data. Here there are 16 points, thus removing starting 3 and last 3 values will almost do the job. I am not writing the data again after removing. I am just wrting the final answer. After you remove those 6 values, there will be 10 values, and mean = Sum of all the values/10

A -> 23.34  

B-> 20.68

C-> 21.02

D -> 20.74

Quartiles

A -> First : 21.25 , Third : 25

B-> First : 19.8 , Third : 21.9

C-> First : 20.65 , Third : 21.475

D->First : 20.2 , Third : 21.475

Standard deviation

A ->2.72

B->1.28

C-> 0.40

D-> 0.72

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.