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Mathematics
Changing Shape and Center staberta:
28 , 29 , 27 , 27 , 29 , 24 , 30 , 20 , 30 , 32 , 24 , 26 , 26 , 26 , 20 , 33 , 25 , 24 , 23 , 19 , 26 , 24 , 24 28,29,27,27,29,24,30,20,30,32,24,26,26,26,20,33,25,24,23,19,26,24,24. 27 , 25 , 25 , 25 , 27 , 27 , 25 , 25 , 24 , 23 , 26 , 26 , 35 , 22 , 28 , 33 , 22 27,25,25,25,27,27,25,25,24,23,26,26,35,22,28,33,22
(a) Create a kivogram for the date widh bis waks of 4. Make an obsernation about the ahape of the graph. Would yoe ug that the graple is selicindy spmentric, or does it heve a loeger tall oe oee sibe thas the ocher?
(b) Create a boxplot for the data. Compare the boxplot to the histogram. What do you notice?
(c) Calculate the mean and the median of the data. Draw vertical lines on the histogram for the mean and the median and label each one.
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(a) The kivogram for the data with bin width of 4 is:
15 |
16 |
17 |
18 |
19 | *
20 | ***
21 |
22 | *****
23 | ***
24 | ********
25 | *********
26 | **********
27 | ********
28 | *
29 | **
30 | ***
31 |
32 | *
33 | *
34 |
35 | *
Observation: The graph is skewed to the right, with a longer tail on the right side and most of the data concentrated on the left side.
(b) The boxplot for the data is:
|___
|
___|___
_______|______|_______|________
|______|
|
20
25.5
30
Comparison with histogram: The boxplot shows the same information as the histogram, such as the median, quartiles, and outliers, but in a different format. The box in the boxplot represents the middle 50% of the data and the whiskers extend to the rest of the data, excluding outliers. The histogram shows the frequency of the data in each bin.
© Mean: 1 46 ( 28 + 29 + + 22 + 28 + 33 + 22 ) = 25.5 (1)/(46)(28+29+cdots+22+28+33+22)=25.5
Median: The median is the middle value in the ordered data set. There are 46 data points, so the median is the average of the 23rd and 24th values, which are both 25.
Vertical lines on the histogram:
|
|
|
|
| *
| ***
|
| *****
| ***
| ********
| *********
| ********** |
| ********|
| *
| **
| ***
|
| *
| *
|
| *
|___*_______*
20
25.5
30
Median Mean
Note: I labeled the mean and median with arrows, but vertical lines can also be used. The mean and median are close together and both are within the middle 50% of the data as shown by the boxplot.
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