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Questions and Answers
Questions and Answers
For the following frequency distribution of exam scores, how many students had scores lower than X = 80?
For the following frequency distribution of exam scores, how many students had scores lower than X = 80?
- 2
- 3 (correct)
- 7
- 8
For the following distribution, how many people had scores less than X = 20?
For the following distribution, how many people had scores less than X = 20?
- 5
- 11
- 12
- 10 (correct)
For the following distribution, how many people had scores greater than X = 14?
For the following distribution, how many people had scores greater than X = 14?
- 5
- 7 (correct)
- 11
- 10
For the following distribution, what is the width of each class interval?
For the following distribution, what is the width of each class interval?
What kind of frequency distribution graph shows the frequencies as bars, with no space between adjacent bars?
What kind of frequency distribution graph shows the frequencies as bars, with no space between adjacent bars?
What kind of frequency distribution graph shows the frequencies as bars that are separated by spaces?
What kind of frequency distribution graph shows the frequencies as bars that are separated by spaces?
What term is used to describe the shape of a distribution in which the scores pile up on the left-hand side of the graph and taper off to the right?
What term is used to describe the shape of a distribution in which the scores pile up on the left-hand side of the graph and taper off to the right?
For the scores shown in the accompanying stem and leaf display, what is the highest score in the distribution?
For the scores shown in the accompanying stem and leaf display, what is the highest score in the distribution?
If the following scores were placed in a stem and leaf display, how many leaves would be associated with a stem of 6?
If the following scores were placed in a stem and leaf display, how many leaves would be associated with a stem of 6?
It is customary to list the score categories in a frequency distribution from the highest down to the lowest.
It is customary to list the score categories in a frequency distribution from the highest down to the lowest.
A grouped frequency distribution table lists one interval as, 20-29. The width of this interval is 9 points.
A grouped frequency distribution table lists one interval as, 20-29. The width of this interval is 9 points.
Construct a frequency distribution for the blood types for 40 people.
Construct a frequency distribution for the blood types for 40 people.
Find the value of the missing entry in the relative frequency table.
Find the value of the missing entry in the relative frequency table.
If a histogram has a bar that is taller than the others, then:
If a histogram has a bar that is taller than the others, then:
Identify the overall shape of the distribution from the given stem and leaf plot.
Identify the overall shape of the distribution from the given stem and leaf plot.
Which of the following is a technique for improving a stemplot with very few stems but many leaves?
Which of the following is a technique for improving a stemplot with very few stems but many leaves?
What is the difference between a bar chart and a histogram?
What is the difference between a bar chart and a histogram?
The class width is the difference between:
The class width is the difference between:
Find (a) the number of classes and (b) the class width for community hospital admissions.
Find (a) the number of classes and (b) the class width for community hospital admissions.
Find (a) the number of classes and (b) the class width for live multiple births.
Find (a) the number of classes and (b) the class width for live multiple births.
A ____________________ is a bar graph whose bars are drawn in decreasing order of frequency or relative frequency.
A ____________________ is a bar graph whose bars are drawn in decreasing order of frequency or relative frequency.
Determine the original set of data from the given stem and leaf plot.
Determine the original set of data from the given stem and leaf plot.
Compute the relative frequency for the back, elbow, and knee categories respectively.
Compute the relative frequency for the back, elbow, and knee categories respectively.
When a data set is skewed left the mean is substantially smaller than median.
When a data set is skewed left the mean is substantially smaller than median.
When a data set is symmetric the mean is roughly equal to the median.
When a data set is symmetric the mean is roughly equal to the median.
When a data set is skewed right the mean is substantially larger than the median.
When a data set is skewed right the mean is substantially larger than the median.
When a data set is symmetric the mean is substantially larger than the median.
When a data set is symmetric the mean is substantially larger than the median.
Questions and Answers
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Study Notes
Study Notes
Frequency Distributions
- To find the number of students with scores lower than a specific value, sum frequencies of intervals below that value.
- For X = 80 in exam scores: Students scoring below 80 equals the sum of intervals 75-79 (2) and 70-74 (1), totaling 3.
- For X = 20 in another distribution, count intervals below 20, which includes the scores 15-19 (5) and 10-14 (4), leading to 10 total.
Class Intervals
- Class interval width calculated as the difference between the upper and lower limits of a class.
- For the interval 20-25, the width is 5.
- Correct class width is crucial for creating accurate frequency distributions.
Graphical Representations
- A histogram displays frequencies as contiguous bars; there is no space between bars.
- A bar graph shows frequencies as separate bars with spaces in between.
- The shape of distribution can be skewed positively (tail on right) or negatively (tail on left).
- A bell-shaped distribution indicates a normal distribution in data.
Stem and Leaf Displays
- The highest score in a stem and leaf display can be identified by finding the largest leaf.
- Count leaves associated with each stem to understand data distribution—stem 6 corresponds to three leaves (62, 64, 66).
Frequency Distribution Characteristics
- It is customary for frequency distributions to be organized from highest to lowest.
- A grouped frequency distribution class width must be calculated accurately to reflect intervals.
Statistical Terminology
- A Pareto chart displays bars in descending order of frequency, aiding in identifying the most significant categories.
- Relative frequency conveys the proportion of each category in comparison to the total.
Data Distribution Analysis
- Left skewed data means mean < median, while right skewed means mean > median.
- Symmetric distributions have closely aligned mean and median values.
- When analyzed, they help understand trends and deviations in data sets.
Classifications and Averages
- A distribution's classification can involve identifying the number of classes and their widths using specific criteria.
- Multiple births data reflects the complexity of statistics through intervals and frequency counts.
Practice Scenarios
- Engaging in exercises to determine class intervals, both through calculations of widths and identification of frequencies, enhances statistical competency.
- Regularly correct affirmations regarding relationships between means and medians across varying distributions solidifies foundational knowledge.
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