Questions and Answers
For the following frequency distribution of exam scores, how many students had scores lower than X = 80?
For the following distribution, how many people had scores less than X = 20?
For the following distribution, how many people had scores greater than X = 14?
For the following distribution, what is the width of each class interval?
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What kind of frequency distribution graph shows the frequencies as bars, with no space between adjacent bars?
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What kind of frequency distribution graph shows the frequencies as bars that are separated by spaces?
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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?
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For the scores shown in the accompanying stem and leaf display, what is the highest score in the distribution?
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If the following scores were placed in a stem and leaf display, how many leaves would be associated with a stem of 6?
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It is customary to list the score categories in a frequency distribution from the highest down to the lowest.
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A grouped frequency distribution table lists one interval as, 20-29. The width of this interval is 9 points.
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Construct a frequency distribution for the blood types for 40 people.
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Find the value of the missing entry in the relative frequency table.
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If a histogram has a bar that is taller than the others, then:
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Identify the overall shape of the distribution from the given stem and leaf plot.
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Which of the following is a technique for improving a stemplot with very few stems but many leaves?
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What is the difference between a bar chart and a histogram?
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The class width is the difference between:
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Find (a) the number of classes and (b) the class width for community hospital admissions.
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Find (a) the number of classes and (b) the class width for live multiple births.
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A ____________________ is a bar graph whose bars are drawn in decreasing order of frequency or relative frequency.
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Determine the original set of data from the given stem and leaf plot.
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Compute the relative frequency for the back, elbow, and knee categories respectively.
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When a data set is skewed left the mean is substantially smaller than median.
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When a data set is symmetric the mean is roughly equal to the median.
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When a data set is skewed right the mean is substantially larger than the median.
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When a data set is symmetric the mean is substantially larger than the median.
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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.
Studying That Suits You
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Description
Test your knowledge of frequency distributions with these flashcards focused on Chapter 2 of your statistics course. Each card presents a different scenario where you calculate the number of students or individuals below a specific score. Perfect for mastering key concepts in statistics!
