Research Methods Part 1 Ch 2
How is "TIME" data depicted?
Observed changing characteristics of the data over time.
A bar graph for QUALITATIVE data, with the bars arranged in DESCENDING order according to frequencies
Pareto Chart
2.1.21 WeightsWeights of statistics students were obtained by a teacher as part of an experiment conducted for the class. The last digit of those weightsweights are listed below. Construct a frequency distribution with 10 classes. Based on the distribution, do the weightsweights appear to be reported or actually measured? What can be said about the accuracy of the results? 0 0 0 0 0 0 0 0 1 1 2 2 3 3 4 4 5 5 5 5 5 5 5 5 5 5 6 8 8 9 9 Part A: Complete the frequency distribution below. Last Digit --> Frequency - 0 ----------> ? - 1 ----------> ? - 2 ----------> ? - 3 ----------> ? - 4 ----------> ? - 5 ----------> ? - 6 ----------> ? - 7 ----------> ? - 8 ----------> ? - 9 ----------> ? Part B: Based on the distribution, do the weightsweights appear to be reported or actually measured? A. The weightsweights appear to be reported because there are disproportionately more 0s and 5s. B. The weightsweights appear to be actually measured because there are disproportionately more 0s and 5s. C. The weightsweights appear to be actually measured because the distribution is uniform. D. The weightsweights appear to be reported because the distribution is uniform. Part C: What can be said about the accuracy of the results? A. They are likely not very accurate because they appear to be actually measured. B. They are likely accurate because they appear to be actually measured. C. They are likely not very accurate because they appear to be reported. D. They are likely accurate because they appear to be reported.
Part A = 0=8, 1=2, 2=2, 3=2, 4=2, 5=10, 6=1, 7=0,8=2, 9=2 Part B = A. The weightsweights appear to be reported because there are disproportionately more 0s and 5s. Part C = C. They are likely not very accurate because they appear to be reported.
2.2.9 The table available below is the frequency distribution for data of the pulse rates (beats per minute) of males. Use the frequency distribution to construct a histogram. Use class midpoint values for the horizontal scale. Do the pulse rates of males appear to have a normal distribution? Part A: Which histogram on the back shows the data? Part B: Since the histogram has ___________________________________, the pulse rates of males __________ to have a distribution that is approximately normal.
Part A = D Part B = - a roughly symmetric "bell" shape, - appear
A graph depicting qualitative data as slices of a circle, size of slice is proportional to frequency count
Pie Chart
What type of distribution includes the same class limits as a frequency distribution, but the frequency of a class is replaced with a relative frequencies (a proportion) or a percentage frequency ( a percent)
Relative Frequency Distribution
How are "OUTLIERS" depicted?
Sample values that lie very far away from the vast majority of other sample values.
A plot of paired (x,y) data with a horizontal x-axis and a vertical y-axis. Used to determine whether there is a relationship between the two variables
Scatter Plot
How is the "DISTRIBUTION" of data depicted?
The nature or shape of the spread of data over the range of values (such as bell-shaped, uniform, or skewed).
What type of graph uses bars of equal width to show frequencies of categories of QUALITATIVE data. Vertical scale represents frequencies or relative frequencies. Horizontal scale identifies the different categories of QUALITATIVE data.
- Bar Graph
what is a graph called when it uses bars of equal width to show frequencies of categories of qualitative data and has two or more sets of bars that are used to compare two or more data sets.
- Multiple Bar Graph
2.1.13-T Use the pulse rates (beats per minute) of males in the accompanying data set to construct a frequency distribution. Begin with a lower class limit of 40 and use a class width of 10. Do the pulse rates of males appear to have a normal distribution? Do the pulse rates of males appear to have a normal distribution? The pulse rates of males __________ a normal distribution because the frequencies start low, increase, and then decrease; and are roughly symmetric.
- appear to have - start low, increase, and then decrease; and are roughly symmetric.
2.1.17-T Refer to the accompanying data set of red blood cell counts (million cells/μL) for males. Construct a frequency distribution. Begin with a lower class limit of 4 and use a class width of 0.5. Using a very loose interpretation of the requirements for a normal distribution, do the red blood cell counts appear to be normally distributed? Using a very loose interpretation of the requirements for a normal distribution, do the red blood cell counts appear to be normally distributed? The frequency distribution _________________ a normal distribution because the frequencies ____________________________
- could reasonably be - start low, increase, and then decrease; and are perfectly symmetric.
3 Reasons for Constructing Frequency Distributions
1. Large data sets can be summarized. 2. We can analyze the nature of data. 3. We have a basis for constructing important graphs.
List 5 important characteristics of data
1. center 2. variation 3. distribution 4. outliers 5. Time
2.2.6 The histogram to the right represents the sepal widths (mm) of a sample of irises. What is the class width? What are the approximate lower and upper class limits of the first class? The class width is __________ mm. For the first class, the approximate lower limit is __________ mm and the approximate upper limit is __________ mm.
= 0.4 mm = 1.5 mm = 1.9 mm
2.2.5 The histogram to the right represents the sepal widths (mm) of a sample of irises. Based on the histogram, what is the number of irises in the sample? There are ___________ irises in the sample.
= 46 irises
What is a histogram?
A graph consisting of bars of equal width drawn adjacent to each other (without gaps). The horizontal scale represents the classes of quantitative data values and the vertical scale represents the frequencies. The heights of the bars correspond to the frequency values. Basically a graphic version of a frequency distribution.
How is the "VARIATION" of data depicted?
A measure of the amount that the data values vary.
How is the "CENTER" of data depicted?
A representative or average value that indicates where the middle of the data set is located.
What are the numbers used to separate classes, but without the gaps created by class limits called?
Class Boundaries
What are the values in the middle of the classes and can be found by adding the lower class limit to the upper class limit and dividing the sum by two called?
Class Midpoints
What type of table shows how a data set is partitioned among all of several categories (or classes) by listing all of the categories along with the number of data values in each of the categories.
Frequency Distribution (or Frequency Table)
What is a relative frequency histogram?
Has the same shape and horizontal scale as a histogram, but the vertical scale is marked with relative frequencies instead of actual frequencies
What are the smallest numbers that can actually belong to different classes called?
Lower Class Limits
What kind of graph shows data that have been collected at different points in time: time-series data
Time-Series Graph
What are the largest numbers that can actually belong to different classes called?
Upper class limits
Frequency polygon vs relative frequency polygon.... What type of polygon uses line segments connected to points directly above class midpoint values
frequency polygon
The presence of ________ can show that we have data from two or more different populations. However, the converse is not true, because data from different populations do not necessarily result in _________ (same as first blank).
gaps
We use a visual tool called a __________ to analyze the shape of the distribution of the data.
histogram
