*you need your book today!!!! chapter 2 · 2013. 9. 6. · 2.1.notebook september 06, 2013 chapter...

2.1.notebook September 06, 2013

Chapter 2:

Organizing Data

*You need your book today!!!!

Florence Nightingale (1820-1910) has been described as the "relevant statistician ." --One of the first to use graphic representations of stats--Improved sanitation in hospitals with charts/diagrams

Her stat reports about the appalling sanitary conditions at Scutari (main British hospital in Crimean War) were taken seriously by the English Secretary of War (Sidney Herbert).

Her recommendations were instituted in military hospitals, and the mortality rate dropped from 42.7% to 2.2%!!


There were no vessels for water or utensils of any kind; no soap, towels, or clothes, no hospital clothes; the men lying in their uniforms, stiff with gore and covered with filth to a degree and of a kind no one could write about; their persons covered with vermin . . . We have not seen a drop of milk, and the bread is extremely sour. The butter is most filthy; it is Irish butter in a state of decomposition; and the meat is more like moist leather than food. Potatoes we are waiting for, until they arrive from France . . .

Early in 1855, because of the defects in the sanitation system, there was a great increase in the number of cases of cholera and of typhus fever among Nightingale's patients. Seven of the army doctors and three of the nurses died. Frostbite and dysentery from exposure in the trenches before Sevastopol made the wards fuller than before. There were over 2000 sick and wounded in the hospital and in February 1855 the deathrate rose to 42%. The War Office ordered the sanitary commissioners at Scutari to carry out sanitary reforms immediately, after which the deathrate declined rapidly until in June it had fallen to 2%.


Florence Nightingale said, "In dwelling upon the vital importance of sound observation, it must never be lost sight of what observation is for.

"It is not for the sake of piling up miscellaneous information or curious facts, but for the sake of saving life and increasing health and comfort."

--Notes on Nursing

Ways to Organize & Present Data

PictographsBar GraphsPie ChartsDot PlotsHistogramsTime SeriesStem Plots

*We will discuss in later chapters.

Frequency DistributionsPareto chartsFrequency PolygonsOgivesBoxnWhisker*Scatter Plots*


PictographsUses a picture or graphic to represent frequency

Frequency Distribution ‐‐ lists each category or class and the number of times it has occurred (frequency).

Two types of Frequency Distributions are:‐‐Categorical ‐‐Grouped


Constructing a Categorical Frequency DistributionThe following is a list of the top 10 saddest children's movies. Pick the one you think is the most sad. Construct a categorical frequency distribution of the class data.

BAMBIOLD YELLERET: THE EXTRATERRESTRIALWHERE THE RED FERN GROWSUPDUMBOCHARLOTTE'S WEB

Constructing a Distribution with small amounts of dataThe following set of N = 20 scores was obtained from a 10point stats quiz. Organize these into a frequency distribution.

8 9 8 7 10 9 6 4 9 87 8 10 9 8 6 9 7 8 8


Constructing a Grouped Frequency Distribution (for large amounts of data)An instructor has obtained the set of N = 25 exam scores shown here. Construct a grouped frequency distribution of the data set using 9 classes.

82 75 88 93 53 84 87 58 72 94 69 84 6191 64 87 84 70 76 89 75 80 73 78 60

Step 1: Find the range of the scores.

Step 2: Divide the range by the # of classes to get the class width .Round UP to the next highest whole number.

Step 3: Begin setting classes by the multiples of the width you're using. Lowest value is 53, so we will start with the number ______ and go up by the width. Be careful: that first number IS counted in the width. Write down class limits.

82 75 88 93 53 84 87 58 72 94 69 84 6191 64 87 84 70 76 89 75 80 73 78 60

ClassLimits

ClassBoundaries Frequency Cumulative Frequency


Step 4: Find the class boundaries by adjusting your class limits by 0.5 in both directions.

Step 5: Fill out your table with class limits, boundaries, and frequencies.

ClassLimits


82 75 88 93 53 84 87 58 72 94 69 84 6191 64 87 84 70 76 89 75 80 73 78 60

ClassLimits


82 75 88 93 53 84 87 58 72 94 69 84 6191 64 87 84 70 76 89 75 80 73 78 60


Your turn!Construct a Grouped Frequency Distribution using 6 classes.

The following are scores from a math test. 65 75 50 67 86 66 62 64 71 4757 74 63 67 56 65 70 87 48 5041 66 73 60 63 45 78 68 53 75

Answers!Construct a Grouped Frequency Distribution using 6 classes.The following are scores from a math test.

65 75 50 67 86 66 62 64 71 4757 74 63 67 56 65 70 87 48 5041 66 73 60 63 45 78 68 53 75

ClassLimits



Histograms are bar graphs for interval or ratio data. The data scale is on the xaxis and the frequency is on the yaxis.

The Histogram

Use the grouped frequency distribution we completed in our example to construct a histogram of the data set.

49.5 54.5 59.5 64.5 69.5 74.5 79.5 84.5 89.5 94.5

1

2

3

4

5

f

EXAM SCORE

The Frequency PolygonFrequency Polygons are also used for interval or ratio data. The data scale is on the xaxis and the frequency is on the yaxis.

Use the grouped frequency distribution we completed in our example to construct a frequency polygon of the data set.

49.5 54.5 59.5 64.5 69.5 74.5 79.5 84.5 89.5 94.5

1

2

3

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f

EXAM SCORE

50 55 60 65 70 75 80 85 90 95


The OgiveOgives are also used for interval or ratio data. The data scale is on the xaxis and the cumulative frequency is on the yaxis.Use the grouped frequency distribution we completed in our example to construct an ogive of the data set.

49.5 54.5 59.5 64.5 69.5 74.5 79.5 84.5 89.5 94.5

cf

EXAM SCORE

5

10

15

20

25

Distribution ShapesHistograms are valuable tools. If the raw data came from a random sample, the resulting histogram should have a shape similar to that of the entire population's shape. This will be a major importance later in this course.

Mounds

haped

Symmetr

ical


Distribution Shapes

Uniform

or

Rectang

ular Dis

tribution

Distribution Shapes

Positive

ly Skewe

d

Skewed R

ight


Distribution Shapes

Negative

ly Skewe

d

Skewed L

eft

Distribution Shapes

Bimodal

Histogr

am

Mode = # that occurs the most


More Practice!

1. What is the difference between a class boundary and a class limit?

2. A data set has values ranging from a low of 10 and a high of 52. What's wrong with using the class limits: 1019, 2029, 3039, 4049 for a frequency distribution?

3. A data set with whole numbers has a low value of 20 and a high value of 82. Find the class width and class limits for a frequency distribution with 7 classes.

More Practice! ANSWERS

1. What is the difference between a class boundary and a class limit?Boundary: halfway point of the space between the upper limit of one class and the lower limit of the next class (can't be data values)Limit: the numbers that separate each of the classes (are data values)

2. A data set has values ranging from a low of 10 and a high of 52. What's wrong with using the class limits: 1019, 2029, 3039, 4049 for a frequency distribution?It does not include all the data (the numbers above 49 to 52).

3. A data set with whole numbers has a low value of 20 and a high value of 82. Find the class width and class limits for a frequency distribution with 7 classes.Class width = (82 20) ÷7 = 8.8 = 9Class Limits: 2028, 2937, 3846, 4755, 5664, 6573, 7482


4. You are a manager of a specialty coffee shop and collect data throughout a full day regarding waiting time for customers from the time they enter the shop until the time they pick up their order.a. What type of distribution do you think would be most desirable for the waiting times: skewed right, skewed left, bellshape symmetrical?

b. What if the distribution were bimodal? What might be an explanation?

4. You are a manager of a specialty coffee shop and collect data throughout a full day regarding waiting time for customers from the time they enter the shop until the time they pick up their order.a. What type of distribution do you think would be most desirable for the waiting times: skewed right, skewed left, bellshape symmetrical?

SKEWED RIGHT: you want most wait times to be short

b. What if the distribution were bimodal? What might be an explanation?

Lots of customers means long wait times (long lines)Few customers means short wait times (short lines)


5. The following data represent salaries, in 1000s of dollars, for employees of a small company. The data have been ordered from lowest to highest.

a. Make a histogram using the class boundaries: 23.5, 69.5, 115.5, 161.5, 207.5, and 253.5.

24 25 25 27 27 29 30 35 35 35 36 3838 39 39 40 40 40 45 45 45 45 47 5252 52 58 59 59 61 61 67 68 68 68 250

10

20

30

40

50

f

Salary in Thousands


b. Look at the last data value. Does it appear to be an outlier (a value that doesn't fit the rest of the values)? Could this be an owner's salary?

24 25 25 27 27 29 30 35 35 35 36 3838 39 39 40 40 40 45 45 45 45 47 5252 52 58 59 59 61 61 67 68 68 68 250



c. Take out the highest value (250). Make a new histogram with the class boundaries: 23.5, 32.5, 41.5, 50.5, 59.5, and 68.5. Does this new histogram represent salaries of the company better than the first one you did?

24 25 25 27 27 29 30 35 35 35 36 3838 39 39 40 40 40 45 45 45 45 47 5252 52 58 59 59 61 61 67 68 68 68 250

2

4

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10

f

Salary in Thousands

6. Certain kinds of tumors tend to recur. The following data represent the lengths of time, in months, for a tumor to recur after chemotherapy (DP Byar, Journal of Urology, vol. 10, pp. 556561). Using 5 classes, construct an ogive.19 18 17 1 21 22 54 46 25 4950 1 59 39 43 39 5 9 38 1814 45 54 59 46 50 29 12 19 3638 40 43 41 10 50 41 25 19 3927 20

cf

Time (months)

10

20

30

40

50

*you need your book today!!!! chapter 2 · 2013. 9. 6. · 2.1.notebook september 06, 2013 chapter...

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