Healthcare Statistics Ch. 2

table title

1) What does data represent? 2) What is the source of the data? 3) When was the data collected?

Percentiles divide the distribution into ____ part(s). a. 1 b. 10 c. 100 d. 1,000

100

The age of all patients diagnosed with cancer during the past year (255 new cases) was recorded. The youngest patient was 3 years old and the oldest was 92. Determine the number of class intervals.

13

Eighteen people sign up to participate in a 5K race and their completion time in minutes is as follows: What is the value of N? a. 5 b. 6 c. 18 d. 37

18

Which term best defines the midpoint of the upper limit of one class and the lower limit of the next class? a. Frequency b. Cumulative frequency c. Class midpoint d. Class boundary

Class boundary

A frequency distribution table may include only some scores in a distribution and each score can fall into more than one class interval. a. True b. False

False

class width

To approximate class width, divide the range by the number of classes desired. (Refer to the example above in which the number of classes chosen was 15.) This calculation will approximate the class width for the distribution.

A limitation of grouping data is loss of detail; however it is an effective way to see the "overall" picture. a. True b. False

True

Grouping data has been facilitated with the aid of high-speed computers and data is easily sorted by many software packages including Excel. a. True b. False

True

Percentile rank (r) = divide the number of values less than r by N x 100. a. True b. False

True

Tables should include a title, headings, data in data cells, and any additional information needed such as a footnote, units of measure, totals, and possibly a table number. a. True b. False

True

The percentile score represents the score that one has to attain to reach a specific percentile. a. True b. False

True

grouped frequency distribution

a distribution used when the range is large and classes of several units in width are needed

Indicate the class boundaries for a class limit of: a. 1 to 5 (compute to the first decimal) to b. 70.5 to 80.5 to c. 6.75 to 7.25 (compute to the first decimal) to

a. 0.5-5.4 b.70-???? c. 6.25-?????

relative frequency and percentage

are calculated similarly as for qualitative data. To calculate the relative frequency for a class, divide the frequency (f) for that class by the sum of all frequencies (total scores in the distribution). The percentage is determined by multiplying the relative frequency by 100.

class

is a category into which a score can be placed. It is a single score in a small distribution and a grouping of scores in a grouped distribution; it is an interval that includes all the values that fall within two numbers, the lower and upper limits. For instance, one class could include all heights from 60 to 64 inches; the next class would include heights from 65 to 69 inches; and so on. Each one of these is called a class interval.

class midpoint

is obtained by dividing the sum of the two limits (or the two boundaries of a class) by 2. In the frequency table above, the class limits of the lowest interval (5-9) has class boundaries of 4.5 to less than 9.5. The class midpoint is 7 .

When working with quantitative data, the difference between the highest value and the lowest value is the ____. a. span b. range c. class d. width

range

Frequency

refers to the number of times the score appears in the array

class limits

the values at the upper and lower ends of a class interval.

table number

Not all tables require a table number. A table number is used to aid the reader in accessing the data.

table headings

(1) Stub (series) heading. A stub (series) heading is the heading of the first column and indicates how the data were interpreted. This could be months of the year, ages, sex of participants, or score limits of a frequency distribution. (2) Column/category headings. These are the subheadings related to the stub heading. Each heading should clearly state what is being displayed.

The number of laboratory tests carried out on 48 patients during their hospital stay (discharged last week) included: 17 2 15 22 31 11 18 5 7 17 3 16 1 12 9 4 6 44 7 18 4 10 14 12 8 13 3 3 8 11 25 29 9 21 36 2 5 6 17 8 3 9 13 9 6 5 9 14 What was the average number of test performed on the 48 patients? (compute to the second decimal)

577/48= 12.02

ungrouped frequency distribution

consists of raw data or a listing of scores from high to low or low to high.

frequency distribution

data organized into classes or categories

range

difference between the highest and lowest score of a frequency distribution.

There are two main reasons for classifying data into a grouped frequency distribution:

(1) Bring order to chaos. Listing scores according to size reduces the disorganization present in the original array of data. (2) Condense data to a more readily grouped form—more concise and useful.

additional information

(1) Footnote. If codes, abbreviations, acronyms, or symbols are unavoidable, an explanatory footnote should be included. (2) Units of Measure. Units of measure (lbs or gms, ages in months or years) should be documented to prevent misinterpretation of the data presented. (3) Totals. Totaling data in rows and columns often provides a simple method of cross-checking the accuracy in a table. If percentages are used, it is recommended they be presented as whole numbers and the total (100%) indicated.

A questionnaire was given to all patients discharged from a rehabilitation facility. The respondents were asked to rate the care or service they received. The choices included excellent (E), good (G), fair (F), and poor (P). A total of 75 responses were tabulated as follows: E G G E F E G G E F E E G G P E G F E GGG E E P E G GG E G F E G G F E E P E G GGP E G G E F E E E G G F E F G E E G GGGGG P E E F G E E F G Construct a qualitative frequency distribution and include a frequency column, relative frequency column, and frequency percentage column. 1a. Determine the relative frequency (compute to the third decimal) and frequency percentage (compute to the first decimal) % for "excellent" responses. 1b. Determine the relative frequency (compute to the third decimal) and frequency percentage (compute to the first decimal) % for "good" responses. 1c. Determine the relative frequency (compute to the third decimal) and frequency percentage (compute to the first decimal) % for "fair" responses. 1d. Determine the relative frequency (compute to the third decimal) and frequency percentage (compute to the first decimal) % for "poor" responses.

1a. Determine the relative frequency (compute to the third decimal) 0.373 and frequency percentage (compute to the first decimal) 37.3% for "excellent" responses. 1b. Determine the relative frequency (compute to the third decimal) 0.427 and frequency percentage (compute to the first decimal) 42.7% for "good" responses. 1c. Determine the relative frequency (compute to the third decimal) 0.133 and frequency percentage (compute to the first decimal) 13.3% for "fair" responses. 1d. Determine the relative frequency (compute to the third decimal) 0.067 and frequency percentage (compute to the first decimal) 6.7% for "poor" responses.

Using the scores of 30 students on a statistics test determine the range. 75 52 80 96 65 79 71 87 93 95 69 72 81 61 7686 79 68 50 92 83 84 77 64 71 87 72 92 57 98

48

Which of the following applies when designing a frequency distribution? a. The number of classes should generally be from five to fifteen. b. All scores from the entire range should be included. c. Each data entry should fall into only one category. d. All of the above

All of the above

Which of the following is not a common component of a table? a. Title b. Author c. Heading d. Table number

Author

A blood sample was drawn from 50 smokers between the ages of 45 and 65 and the serum cholesterol level recorded. The values are as follows: 291 285 273 270 268 260 260 256 254 252 251 248 247 243 241 240 240 239 238 238 238 235 234 233 233 231 230 229 227 227 226 223 222 221 221 219 217 214 212 209 207 205 199 198 188 185 179 177 165 158 Calculate the range and the number of class intervals if 10 scores are grouped in each interval.

Calculate the range 133 and the number of class intervals 14 if 10 scores are grouped in each interval.

Which of the following is a limitation of percentile scores? a. Percentile scores are equally divided up and down the percentile scale. b. Percentile scores are not equally divided up and down the percentile scale.

Percentile scores are not equally divided up and down the percentile scale.

Which of the following refers to data that is unranked and ungrouped? a. Raw b. Tallied c. Relative d. Invalid

Raw

"N" denotes which of the following? a. Mean b. Population size c. Sample size d. Median

Sample size

table cells (data)

The appropriate data elements are entered in the table under the appropriate heading.

raw data

The original data as it was collected.

When determining class width which of the following statements is correct? a. The smaller the interval size, the more detailed the interpretation. b. The smaller the interval size, the less detailed the interpretation. c. The larger the interval size, the more detailed the interpretation. d. There is no relationship between internal size and detail of interpretation.

The smaller the interval size, the more detailed the interpretation.

Percentiles (centiles, deciles, quartiles) divide a distribution into 100 equal segments. a. True b. False

True

When determining class limits, any convenient number equal to or less than the smallest value in the data set can be used to set the lower limit for the first class. a. True b. False

True

Determine the approximate number of classes resulting if: a. A class interval size of 5 is used for a range of 20 to 85. b. A class interval size of 3 is used for a range of 8 to 50. c. A class interval size of 7 is used for a range of 43 to 113. d. A class interval size of 2 is used for a range of 131 to 160. (compute to the first decimal)

a. 13 b. 14 c. 10 d. 14.5

The number of days a patient was hospitalized with a diagnosis of traumatic injury were recorded as follows: 20 19 18 18 17 17 17 15 15 14 14 14 13 13 12 11 11 10 10 1010 9 9 8 8 8 8 8 7 7 7 6 6 6 6 6 6 6 5 5 5 5 5 5 5 5 44 4 4 4 4 4 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 a. What is the value of n? b. Calculate the percentage of scores with stays greater than one week. (compute to the second decimal) % c. Calculate the percentage of scores with stays greater than two weeks. % d. Determine the percentile rank for a stay of nine days. th e. Determine the percentile rank for a stay of three days. st

a. 75 b. 37.33 c. 12 d.

The age of a patient at the time of diagnosis of colon cancer was tracked—50 males and 50 females. The ages are: M: 91 87 87 85 83 81 80 79 78 77 75 75 74 73 72 72 71 71 70 69 69 68 66 66 65 63 63 63 62 62 62 61 61 61 60 60 59 59 57 56 55 55 53 53 51 48 45 39 38 29 F: 94 93 92 90 89 88 87 86 86 85 85 83 81 79 79 78 77 77 76 76 76 76 75 74 74 73 72 72 71 70 68 68 67 66 66 65 65 6564 64 64 63 60 59 58 55 54 53 51 48 a. Calculate the range for males , females , and combined . b. Calculate the average age for men (compute to the second decimal) . c. Calculate the value for:85th percentile for the combined ages. Percentile for an age of 60 for females. the Percentile for an age of 75 for males. th

a. Calculate the range for males 62, females 46, and combined 65. b. Calculate the average age for men (compute to the second decimal) 65.18 c. Calculate the value for: 85th percentile for the combined ages 83 Percentile for an age of 60 for females. 14th Percentile for an age of 75 for males. 76th

The diastolic blood pressure (in mm Hg) of 84 patients with hypertension was: 88 98 78 84 77 81 90 82 75 72 92 85 92 77 84 77 82 10092 88 74 80 95 90 87 80 83 77 86 80 88 90 79 82 93 10080 85 96 85 90 84 82 95 88 97 80 88 94 92 88 96 90 10388 86 84 90 98 88 86 95 97 88 75 82 90 98 84 97 84 10288 78 80 82 86 90 85 95 88 86 90 101Based on this information, construct a frequency distribution in order to answer the following questions. a. Calculate the range. b. Calculate the value of:(1) First quartile score. (compute to whole number) (2) Third quartile score. (compute to whole number) (3) 90th percentile score. (compute to the first decimal) (4) Percentile rank of a score of 81. th(5) Percentile rank of a score of 87. th

a. Calculate the range. 31 b. Calculate the value of: (1) First quartile score. (compute to whole number) 82 (2) Third quartile score. (compute to whole number) 92 (3) 90th percentile score. (compute to the first decimal) (4) Percentile rank of a score of 81. 20th (5) Percentile rank of a score of 87. 48th

Please use the information below for the following questions: Twenty pediatric patients were asked if they live with both parents (B), mother only (M), father only (F), or someone else (S). The responses were as follows: M B B M F S B M F M B F B M M B B F B M

a. Determine the frequency for patients who live with both parents 8, mother only 7, father only 5, someone else 1. b. Determine the relative frequency (compute to two decimal places) for patients who live with both parents 0.40, mother only 0.35, father only 0.20, someone else 0.05. c. Determine the frequency percentage for patients who live with both parents 40%, mother only 35%, father only 20, someone else 5%. d. Would you expect a score of 85 to fall above or below the 85th percentile? Would you expect a score of 70 to fall above or below the 60th percentile?

Using the scores of 30 students on a statistics test answer the following questions: 75 52 80 96 65 79 71 87 93 95 69 72 81 61 7686 79 68 50 92 83 84 77 64 71 87 72 92 57 98 Using the scores of 30 students on a statistics test answer the following questions: 75 52 80 96 65 79 71 87 93 95 69 72 81 61 76 86 79 68 50 92 83 84 77 64 71 87 72 92 57 98 a. Determine the frequency for score limits of: 50-54 , 55-59 , 60-64 , 65-69 , 70-74 , 75-79 , 80-84 , 85-89 , 90-94 , 95-99 b. Determine the relative frequency (compute to the second decimal) for score limits of: 50-54 , 55-59 , 60-64 , 65-69 , 70-74 , 75-79 , 80-84 , 85-89 , 90-94 , 95-99 c. Determine the frequency percentage (compute to the second decimal) for score limits of: 50-54 , 55-59 , 60-64 , 65-69 , 70-74 , 75-79 , 80-84 , 85-89 , 90-94 , 95-99

a. Determine the frequency for score limits of: 50-54: 2 55-59: 1 60-64: 2 65-69: 3 70-74: 4 75-79: 5 80-84: 4 85-89: 3 90-94: 3 95-99: 3 b. Determine the relative frequency (compute to the second decimal) for score limits of: 50-54: 0.07 55-59: 0.03 60-64: 0.07 65-69: 0.10 70-74: 0.13 75-79: 0.17 80-84: 0.13 85-89: 0.10 90-94: 0.10 95-99: 0.10 c. Determine the frequency percentage (compute to the second decimal) for score limits of: 50-54: 6.67 55-59: 3.33 60-64: 6.67 65-69: 10 70-74: 13.33 75-79: 16.67 80-84: 13.33 85-89: 10 90-94: 10 95-99: 10

Please use the information below for the following questions: A group of 25 people signed up for a weight-loss class. Each individual was asked why they wanted to lose weight. The choices were: H (health reasons); C (cosmetic reasons); or O (other). The results were as follows: H H C H O C C H C O O H C H H C H H O H H O C H C

a. determine the frequency for health 12, cosmetic 8, and other 5. b. determine the relative frequency (compute to 2 decimal places) for health .48, cosmetic 0.32, other 0.20. c. determine the frequency percentage for health 48%, cosmetic 32%, and other 20%

The term "____" refers to the number of times the score appears in the array. a. distribution b. distribution c. interval d. frequency

frequency

class boundaries

is the midpoint of the upper limit of one class and the lower limit of the next class.

cumulative frequency

is the sum of the frequencies, starting at the lowest interval and including the frequencies within that interval.

The term "____" is best defined as "relative status in a group." a. rank b. quartile c. decile d. percentile

rank

frequency distribution table

table of data in a frequency distribution