QUESTION 2 - Parts A&B) A baseball coach is considering two different companies for ordering team jerseys. Guy's Graphix cha
rges $30 to create the artwork for the team logo plus $7.50 per jersey. Patty's Printing charges $50 to create the artwork for the team logo plus $5.50 per jersey.
1 answer:
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Given data is 54, 59, 35, 41, 46, 25, 47, 60, 54, 46, 49, 46, 41, 34, 22
Arranging it in increasing order:
22 25 34 35 41 41 46 46 46 47 49 54 54 59 60
Number of data items, n=15.
Finding Median, First Quartile, and Third Quartile
22 25 34 35 41 41 46 46 46 47 49 54 54 59 60
Now finding First Quartile from set: 22 25 34 35 41 41 46
Q₁ = middle term i.e. 35
Now finding Third Quartile from set: 46 47 49 54 54 59 60
Q₃ = middle term i.e. 54
So we have Q₁ = 35, M = 46, and Q₃ = 54. Lower bound is 22 and Upper bound is 60.
While drawing the given data on number line and marking First quartile, Median, Third quartile on number line. We can clearly observe that option A matches with given data points.
Hence, option A i.e. Box-plot A is the correct choice.
Answer:
(a) For the stem-and-leaf plot, we need to organise all data in columns, one column is the stem and a second column is the leaf, but in this case, stems are going to be the digits to the left of the decimal point, and leafs are the digits to the right of the decimal point:
<u>Stem</u> <u> Leaf </u>
0 2 2 2 3 3 4 5 7
1 0 2 3 5 5 8
2 0 3 5
3 0 3
4 0 5 7
5 0 5 6 9
6 0 0 0 5
(b) Relative frequency distribution.
Remember that, a relative frequency is calculated dividing the absolute frequency by the total data, in this case, we approximated to the hundredth.
Length of life Absolute Frequency Relative Frequency % Relative Freq.
0.2 3 0.1 10
0.3 2 0.07 7
0.4 1 0.03 3
0.5 1 0.03 3
0.7 1 0.03 3
1.0 1 0.03 3
1.2 1 0.03 3
1.3 1 0.03 3
1.5 2 0.07 7
1.8 1 0.03 3
2.0 1 0.03 3
2.3 1 0.03 3
2.5 1 0.03 3
3.0 1 0.03 3
3.3 1 0.03 3
4.0 1 0.03 3
4.5 1 0.03 3
4.7 1 0.03 3
5.0 1 0.03 3
5.5 1 0.03 3
5.6 1 0.03 3
5.9 1 0.03 3
6.0 3 0.10 10
6.5 1 0.03 3
Total 30
(c)
To calculate the sample mean we need to sum all number, which results: 83.9. Then, we divide this result to the total 30, which result: 2.80.
The sample range is the difference between the highest and the lowest value: 6.5 - 0.2 = 6.3.
The sample standard deviation is calculated trough the following process:
Step 1: Subtract the mean from each number.
Step 2: Square each result.
Step 3: Add the squared deviations.
Step 4: Divide the sum by one less the total.
Step 5: Take the square root, and there you have it.
Doing this steps, the result is 2.22.
This last process is attached:
