statistics mod 4 part 2

What is the median number of minutes a patient spends waiting during emergency room visits?

The median is indicated by the line that bisects the rectangular box of the box plot. This line is labeled 55; therefore, the median is 55.

What is the minimum value in the data set?

he minimum data point is indicated by the left-most data point indicated on the left stem of the box plot. This data point is labeled 5.

Outliers do not often affect the mean measure of center. True or False?

This is a false statement. Outliers can heavily affect the mean in a distribution. When a distribution is skewed, the mean value will see a direct impact.

Based on the box plot below, approximately what percent of patients represented in this data set have a blood platelet count less than 120 ?

Looking at the box plot, Q1 is approximately 120 . As we know 25% of the data falls below Q1 , we can determine that 25% of the patients represented in this data set will have a blood platelet count below 120 .

An RN was researching reported drug use in people 12 or older for a report she was putting together for her team. She found that The National Survey on Drug Use and Health reported on the number of people 12 and older, by state, who used drugs over the past month. The data reported was collected in 2014 . The lowest drug use rate was 6.27 (Iowa), and the highest was 15.19 (District of Columbia). When presenting the data, she did not want the decimal values to get lost, since they were key to ranking the states by drug use. What display of the drug use rates would you suggest she use? a. Histogram b. Pie Chart c. Stem plot d. Box Plot

stem plot is a good choice as you can see the distribution of the data and the values are preserved.

Anatomy of a Box Plot

Box plots have four parts: the first whisker, two rectangles, and another whisker. Regardless of size, each part represents 25% of the data.

What is the value of the third quartile?

The value of the third quartile (Q3)is indicated on a box plot by the right side of the box. In this box plot the third quartile (Q3) is 70.

Extreme Values in a Skewed Distribution

We refer to values in a histogram that come after a gap as extreme values and possible outlier Even if the data is skewed, that does not necessarily mean that the data to the far right (or left) are outliers. What is important to note is how outliers influence measures of center and spread.

Box plots

also known as box-and-whisker plots or hinge plots, show the distribution or shape of a data set. Box plots are useful when showing the variability and spread within a data set because they take into account median and quartiles rather than averages. (Recall the discussion on quartiles on assignment 4.05.2)

Five-number Summary

A box plot is a convenient way to show five important statistical values: minimum, maximum, first quartile, median, and third quartile. As previously mentioned, these five values are often referred to as a five-number summary of a data set. Many statistical outputs from technology, such as calculators, computer programs, or other software, have five-number summary displays built in. Box plots can either be displayed horizontally or vertically

Find the range of the following data set: 29, 31, 4, 24, 14, 61

The correct answer is c. 61−4=57 .

You are examining a set of data. The mean of the data set is 32 . The data is normally distributed. Approximately 68% of all values fall between 23 and 41 . Approximately 95% of all values fall between 14 and 50 . What is the best estimate for the standard deviation of this data set?

9 Following the empirical rule, we know that approximately 68% of all values are within one standard deviation of the mean, and approximately 95% of all values are within two standard deviations of the mean.

You are designing a study of the number of hours worked by nurses in a particular hospital. You are especially interested in knowing if there are any outliers in the data, as well as the median number of hours worked and the approximate distribution of the data. Which graphical display would satisfy your needs? a. Bar chart b. Histogram c. Stem plot d. Box plot

A box plot is a good display to use to show the shape of a data set, as well as outliers (if any).

In a study on the root cases of medication dispensing errors, the authors included the following data, from interviews, on the cause of mistakes. The most common causes were being busy ( 28.1% ), being short staffed ( 16.8% ), being subject to time constraints ( 15.2% ), fatigue of health care providers ( 15% ), interruptions during dispensing ( 13.4% ) and look alike/sound alike medications ( 11.5% ). Norman, a registered nurse doing a presentation on dispensing errors, wanted to convey this data to his department. What display should he use? a. Pie chart b. Histogram c. Stem plot d. Box plot

A pie chart is a good display in this case. The data is categorical and there are not too many categories.

Using a Two-Dimensional Figure to Represent a One-Dimensional Measurement

Another common source of misrepresentation is the use of a two-dimensional figure to represent a one-dimensional measurement. For example, suppose we have data showing the average healthcare spending per person in the U.S. increased from $146 in 1960 to $9,532 in 2014 . If we use a bar graph, it might look like this: If instead of using a bar graph, we use a two-dimensional figure such as a circle or a rectangle, or a three-dimensional figure such as a cylinder or a rectangular prism, we can create the false impression of greater-than-real differences. The reason is that our eyes see area (in the case of two-dimensional figures) and volume (in the case of three-dimensional figures). This distorts the true differences we are trying to illustrate.

Omitting Axis Labels or Units

Another example of graphs that can misrepresent data are graphs that omit labels or units, such as the pie chart displayed below. Without the percentages for each of the sections of the pie chart, it is difficult to determine which nursing specialty is the largest, and which is the smallest

When the data skews in one direction or another, it is often best to use median and interquartile range to describe the center and spread of the data. Mean and standard deviation are more appropriate measures of center and spread for symmetrical data. The following table summarizes the preferred measures of center and the measures of spread for normal and skewed distributions.

Distribution Skewed Measures of Center Median Measures of Spread Range or IQR Distribution Normal Symmetric Measures of Center Mean Measures of Spread v]Standard Deviation

Examine a skewed-right distribution below:

Due to the fact that this distribution skews to the right, the most extreme values are on the right side of the distribution. These extreme values, or possible outliers, have an effect on the measures of center.

Q1 :

First arrange the data from least to greatest: 105,115,117,117,119,120,121,123,123,125,128,128,131,135,136,141,142,143,158,169. Q1 is the mid-point of the first half of the data set: 105,115,117,117,119| 120,121,123,123,125 | 128,128,131,135,136,141,142,143,158,169. This value is half-way between 119 and 120. 119+1202=119.5. Therefore, Q1=119.5.

Based on the box plot below, what percent of the class scored between 75 and 85 on the algebra exam?

From this box plot we see the median value is equal to 75 , and Q3 is equal to 85 . Since we know in a box plot that 25% of the data falls between the median and Q3 , we can determine that 25% of the class scored between 75 and 85 on the algebra exam.

Extreme Values in a Symmetric Distribution

If a distribution is symmetric, such as a bell-curve, a u-curve, or a uniform distribution, there will be roughly similar extreme values on either side of the distribution. That is to say that a symmetric distribution will have similarly extreme positive and negative values. Examine the bell-curve below: Here, we know that there is equal "pull" coming from the data on both sides. As a feature of symmetric distribution, there should not be many extreme outliers on one side of the distribution but not the other. Therefore, our measures of center (mean, median, mode), will all be roughly in the middle of the histogram, at the peak of the data. Skewed data is often more complicated to measure than symmetric data, though.

The Massachusetts Nursing Association published Nurses' Six Rights for Safe Medication Administration: The right to a complete and clearly written order The right to have the correct drug route and dose dispensed The right to have access to information The right to have policies on medication administration The right to administer medications safely and to identify problems in the system The right to stop, think, and be vigilant when administering medications A senior nurse supervisor sent out a one-question survey to the 1505 nurses at her hospital asking "Are you able to exercise each of these rights in the course of your daily responsibilities?" The six rights were listed, and respondents had to indicate a "Yes/No" for each. The supervisor is planning to display this data in a histogram. Is this the appropriate graph choice? a. Yes b. No

No a histogram is not the correct choice as it is for continuous data; this data is categorical.

The number of cardiograms performed each day at an outpatient testing center was recorded for three weeks. You are asked to recommend a method for displaying the results graphically so that the shape of the data can be seen, and each data value is also visible. What would be the best choice among the following? (Enter the letter that corresponds with your choice.) a. Bar chart b. Histogram c. Scatterplot d. Stem plot

Stem plot is the best choice as these types of graphs show the shape of a data set and each data value.

Which measure of center applies best to skewed distribution?

The answer is a. Because the mean can be largely affected by extreme values on either side of a distribution, median is the most appropriate measure of center for a skewed distribution.

The data set below includes the ages of those working in an office. Make a Stemplot for the following data and identify which value in the data set may be an outlier? 19 b. 38 c. 66 d. None of the above

The answer is a. While 19 is a possible outlier (since there is a gap in the stem plot), it is worth checking this with the 1.5 IQR criterion. Doing this shows that it is not actually an outlier.

The distribution below displays the heights of students in Mr. Carroll's ninth grade math class. Which value in the data set would be considered a possible outlier?

The answer is d. Looking at the data above, the 76 - 78 range would be a possible outlier because it is significantly distant from the other values.

Find the mean of the following data set: 69, 2, 7, 10, 28, 21, 16, 40, 86

The correct answer is b. (69+2+7+10+28+21+16+40+86)÷9=279279÷9=31 31 mean is adding all the number and dividing by how many numbers

There is a set of data containing five numbers. You order these five numbers from least to greatest. The middle number (the third largest and third smallest) is 54 . 23, 36, 54, 58, 65 What does the number 54 represent in this data set?

The correct answer is b. The median is the midpoint of a data set, when ordered from least to greatest.

What is the mode of a set of data values?

The correct answer is c. The mode is the most frequent value in a data set.

Five-number Summary

The far left side of the box plots represents the minimum value of the data set. In the above example, this is 60 . The left whisker represents the lower 25% of the data. In this example, that is from 60 to 70 . That means 25% of students scored between 60 and 70 on the algebra exam. The first part of the box represents the next 25% of the data. It is shaded blue in the above box plot. So another 25% of the students scored between the Q1 of 70 and the median of 75 . The line in the middle of the box is the median ( Q2 ). That means 50% of the data is below this point, and 50% of the data is above this point. In the above example, 50% of students scored below 75 and 50% scored above 75 . The second part of the box represents the next 25% of the data. It is shaded orange in the above box plot. In our example, we see that 25% of the students scored between the median of 75 and the Q3 of 85 . The right whisker represents the upper 25% of the data. In the above example, we can see that 25% of students scored between 85 and 100 on the algebra exam. The far right side of the box plots represents the maximum value of the data set. In the above example, this is 100 .

Consider the following vertical box plot that illustrates the lengths found in a population of sharks.

The top of the line is the maximum value in the data set; in the above example, the maximum value is approximately 18 . The upper limit of the rectangular box, shaded in purple in the above example, represents the third quartile ( Q3 ). The line in the middle of the rectangle (in the above example, this line is indicated where the green and purple shaded areas of the rectangle meet) is the second quartile ( Q2 ) or median. The lower limit of the rectangular box (in the above example, shaded in green) represents the first quartile ( Q1 ). The bottom of the line represents the minimum value of the data set; in the above example, this is approximately 7.5 .

What is the value of the first quartile?

The value of the first quartile (Q1)is indicated on a box plot by the left side of the box. In this box plot the first quartile (Q1) is 15.

A 3-year longitudinal study was conducted to investigate survival rates for patients who suffered cardiac arrest during their stay in the hospital. In 2013 among 86,748 patients who had cardiac arrest during their hospital stay, 58,593 who suffered cardiac arrest survived. In 2014 among 82,523 patients who had cardiac arrest during their hospital stay, 52,931 who suffered cardiac arrest survived. In 2015 among 84,169 patients who had cardiac arrest during their hospital stay, 55,475 who suffered cardiac arrest survived. 1. What type of variable is in this study? Categorical Quantitative Cannot be determined

The variable in this study is a categorical variable.

Changing the Scale of Axis Labels

This graph shows the number of admissions per year for three hospitals. Do you notice anything wrong with this graph? Compare it to the following: The number of admissions per year for three hospitals. The second graph displays the same data. What's the difference between the two graphs? In the first graph, the differences between the hospitals' admissions appear to be greater than they do in the second graph. The reason is that the vertical scale does not start at zero. This is also known as truncating which exaggerates the differences between the three hospitals.

Mode is a measurement not often affected by outliers. True or False?

This is a true statement. Mode measures the most frequent value in a data set. A significant outlier would not necessarily affect the mode of a data set.

Outliers and Choosing Measures

When looking at data, it is productive to look for outliers—observation points (numbers) that are distant from other observations. When outliers are detected, we can try to figure out what leads to these results. We examine our collection techniques, and the data itself, and determine whether the number is incorrect or faulty in some way. We can also determine whether a figure is an outlier because it describes something that does not belong in the study. An outlier may even be correct, but it is helpful to identify any outliers and determine whether they should be used, or whether their existence is indicative of something that has gone wrong.

What is the maximum value in this data set?

maximum data point is indicated by the right-most data point indicated on the right stem of the box plot. This data point is labeled 95.

Which of the following represent the five values included in the five-number summary of a data set?

minimum, first quartile, median, third quartile, maximum

Based on the following box plot, what percent of emergency room visits have a waiting time that is less than 70 minutes?

nswer is a. We know that each part of the box plot represents 25% of the data and that 70 minutes represents Q3 . As 75% of the data falls below Q3 , we can determine that 75% of emergency room visits have a waiting time that is less than 70 minutes.