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PSYCH 211/D > Chapter 3 > Flashcards

Chapter 3 Flashcards

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1
Q

Define BEDMASS.

A

BEDMASS is an acronym that represents the order of operations in mathematics: Brackets, Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

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2
Q

Provide an example of a linear equation that can be solved using BEDMASS.

A

An example is x = 5 + 3^2 - (15 + 8).

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3
Q

Define mode in the context of measures of central tendency.

A

Mode (Mo) is the most frequently occurring value in a distribution.

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4
Q

Describe the median and its significance in a dataset.

A

The median (Mdn) is the point that divides the distribution in half, representing the score at or below which 50% of the scores lie.

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5
Q

How is the mean calculated in statistics?

A

The mean (μ) is calculated as the arithmetic average of all the scores in a dataset.

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6
Q

How does the median differ from the mean?

A

The median is the middle value that divides the dataset in half, while the mean is the average of all values.

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7
Q

Describe a scenario where the mode would be the most useful measure of central tendency.

A

The mode is particularly useful in categorical data where we want to identify the most common category or value.

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8
Q

What does it mean if a dataset has no mode?

A

If a dataset has no mode, it means that no value occurs more frequently than others, indicating a uniform distribution.

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9
Q

How can the mean be affected by outliers in a dataset?

A

The mean can be significantly affected by outliers, as extreme values can skew the average higher or lower.

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10
Q

Define the term ‘typical value’ in relation to measures of central tendency.

A

A typical value refers to a representative score that summarizes the central point of a dataset, often identified by the mode, median, or mean.

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11
Q

Describe how to calculate the mode for ungrouped data.

A

Locate the most frequent value(s) in the dataset.

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12
Q

Define unimodal data.

A

Unimodal data has one mode, which is the most frequently occurring value in the dataset.

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13
Q

What characterizes bimodal data?

A

Bimodal data has two modes, which are the two most frequently occurring values.

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14
Q

How can you determine the mode from a frequency distribution?

A

Identify the value(s) with the highest absolute frequency.

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15
Q

How is absolute frequency represented in a distribution?

A

Absolute frequency is represented by the count of occurrences for each value.

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16
Q

Describe the process of calculating the mode for grouped data.

A

To calculate the mode for grouped data, first, put the data points into intervals (bins). Then, identify the interval with the most observations, and the mode is the midpoint of that interval.

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17
Q

What is a crude mode in the context of grouped data?

A

A crude mode refers to the mode calculated from grouped data, which may not accurately reflect the most frequently occurring value due to the loss of individual data point details.

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18
Q

Describe the mode in terms of its applicability to data types.

A

The mode is the only measure of central tendency that can be used for nominal data, but it can also be applied to other types of data.

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19
Q

How does the mode relate to extreme scores in a dataset?

A

The mode is not influenced by extreme scores, meaning it remains unaffected by outliers in the data.

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20
Q

Define the mode’s stability across different samples.

A

The mode fluctuates from sample to sample, indicating that it can vary depending on the specific data selected.

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21
Q

Discuss the importance of sampling in relation to the mode.

A

When drawing a sample from a population, the mode can change, highlighting the variability of this measure across different samples.

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22
Q

Define the mean in statistics.

A

The mean is the arithmetic average of a set of values, serving as the balance point of the data.

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23
Q

Describe how scores relate to the mean.

A

Scores below the mean balance out scores above the mean.

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24
Q

How can two distributions have the same mean?

A

Two distributions with different variability can have the same mean despite differing data points.

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25
Q

Explain the significance of the mean in data analysis.

A

The mean serves as a central value that summarizes the data set, providing insight into the overall distribution.

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26
Q

Define the symbol μ in the context of statistics.

A

In statistics, μ represents the mean of a distribution.

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27
Q

What is the significance of N in the mean calculation?

A

N represents the number of values in the distribution, which is used to divide the summation to find the mean.

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28
Q

Define the symbol μ in the context of frequency distribution.

A

μ represents the mean in a frequency distribution.

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29
Q

Describe the process of calculating the mean using frequency distribution.

A

To calculate the mean, multiply each score by its frequency (fX), sum these products (∑fX), and then divide by the total number of values (N) in the distribution.

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30
Q

How is the weighted mean calculated for two exams in a class?

A

To calculate the weighted mean, multiply each exam’s mean by the number of students who took that exam, sum these products, and then divide by the total number of students who took the exams.

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31
Q

Explain the significance of the number of students who dropped the class in calculating the weighted mean.

A

The number of students who dropped the class affects the calculation of the weighted mean because it changes the total number of students contributing to the second exam’s mean.

32
Q

How do you calculate the overall mean when some students drop the class between exams?

A

To calculate the overall mean, adjust the weights of the means by considering the number of students who took each exam, then compute the weighted mean.

33
Q

What does the symbol ∑ represent in the context of calculating the mean?

A

∑ represents summation, which means to add up all the values.

34
Q

What does the term fX refer to in frequency distribution calculations?

A

fX refers to the product of each score and its frequency.

35
Q

Calculate the weighted mean based on the provided means and student counts.

A

The weighted mean is calculated as 62.42 based on the means of the two exams and the number of students who took each.

36
Q

Describe how extreme values affect the mean.

A

Extreme or outlier values in a distribution can significantly influence the mean, making it less representative of the central tendency of the data.

37
Q

Define the relationship between sample size and the stability of the mean.

A

The mean becomes more stable with a greater sample size, as larger samples are more representative of the population.

38
Q

How do different distributions affect the mean?

A

Different distributions can yield different means; for example, Distribution A (1, 2, 2, 2, 3, 4, 1,000,000) has a much higher mean than Distribution B (1, 2, 2, 2, 3, 4, 5) due to the outlier.

39
Q

Explain the significance of sample size in statistical analysis.

A

A greater sample size leads to a more stable mean and a better representation of the population, reducing the impact of outliers.

40
Q

What is the effect of outliers on the mean in a dataset?

A

Outliers can skew the mean, making it higher or lower than the central tendency of the majority of the data points.

41
Q

How does the mean behave across multiple samples from the same population?

A

The mean is generally stable across numerous samples from the same population, indicating consistency in the central tendency.

42
Q

Describe the median in a data set.

A

The median is the midpoint of the distribution, representing the value that separates the higher half from the lower half of the data set.

43
Q

How do you find the median when the number of data points is odd?

A

To find the median with an odd number of data points, arrange the data in order from smallest to largest and take the middle point.

44
Q

How do you calculate the median when the number of data points is even?

A

When the number of data points is even, calculate the median by averaging the two middle values.

45
Q

Define the process of arranging data points for median calculation.

A

The process involves sorting the data points in order from smallest to largest before determining the median.

46
Q

What is the formula for finding the median in an even data set?

A

The formula for finding the median in an even data set is (4th value + 5th value)/2.

47
Q

What assumption is made about middle values when calculating the median?

A

It is assumed that no middle values are repeated when calculating the median.

48
Q

Define the median in a data set.

A

The median is the midpoint of the distribution, found by arranging data points in order from smallest to largest.

49
Q

Describe the process of finding the median.

A

To find the median, arrange the data points in order from smallest to largest, then identify the middle point or average the two middle points depending on whether N is odd or even.

50
Q

Describe the purpose of linear interpolation in calculating the median.

A

Linear interpolation is used to compute the median when the middle value is repeated, allowing for a more accurate representation of the central tendency.

51
Q

How do you identify the lower limit in a dataset for median calculation?

A

The lower limit is identified as the value just below the critical value of the repeated observation; for example, if the critical value is 4, the lower limit would be 3.5.

52
Q

How is the interval width (i) determined for non-grouped data in median calculation?

A

For non-grouped data, the interval width (i) is always considered to be 1.

53
Q

Explain the significance of the number of repeated values (f w) in the median calculation.

A

The number of repeated values (f w) indicates how many times the critical value appears in the dataset, which is essential for determining the median when values are repeated.

54
Q

What is the critical value in the provided dataset for median calculation?

A

The critical value in the provided dataset (1, 2, 2, 4, 4, 4, 7) is 4.

55
Q

How is the critical value determined in a dataset with an odd number of values?

A

The critical value is the middle value of the dataset, which in this case is 4.

56
Q

How does the presence of repeated values affect the determination of the median?

A

Repeated values can influence the cumulative frequency and the calculation of the median, as they may shift the middle point.

57
Q

Describe the process of linear interpolation with grouped data.

A

Linear interpolation with grouped data involves using intervals to estimate values. The critical value is determined by finding the middle value of the data points, which is calculated as N/2. For example, if N = 30, the critical value is between the 15th and 16th values. If the 15th value is too low, the next interval up is used for interpolation.

58
Q

Define the critical value in the context of linear interpolation with grouped data.

A

The critical value in linear interpolation with grouped data is the middle value of the dataset, calculated as N/2. For a dataset with 30 data points, the critical value would be between the 15th and 16th values.

59
Q

What is the significance of the intervals in linear interpolation with grouped data?

A

Intervals in linear interpolation with grouped data allow for the organization of data points into ranges, making it easier to estimate values when exact data points are unknown. They help in identifying where the critical value falls within the grouped data.

60
Q

Do you need to know the exact data points to perform linear interpolation with grouped data?

A

No, you do not need to know the exact data points to perform linear interpolation with grouped data. Instead, you work with the intervals and their corresponding frequencies to estimate values.

61
Q

What is the cumulative frequency and how is it used in linear interpolation with grouped data?

A

Cumulative frequency is the running total of frequencies up to a certain interval. It is used in linear interpolation with grouped data to determine the position of data points within the intervals and to identify the critical interval for interpolation.

62
Q

Explain the role of intervals in grouped data for linear interpolation.

A

Intervals in grouped data provide a range within which data points fall, allowing for estimation of values when exact data points are not available.

63
Q

Define the term ‘critical interval’ in the context of data analysis.

A

A critical interval refers to a specific range of values within a dataset that is used to analyze or summarize data, particularly when determining the position of a median or other statistical measures.

64
Q

Describe how to calculate the lower exact limit of a critical interval.

A

The lower exact limit of a critical interval is calculated by subtracting 0.5 from the lower boundary of the interval. For example, for the interval 10 - 12, the lower exact limit is 10 - 0.5 = 9.5.

65
Q

How is the width of the critical interval determined?

A

The width of the critical interval is determined by subtracting the lower limit from the upper limit of the interval. For the interval 10 - 12, the width is 12 - 10 = 2.

66
Q

How many values are in the interval 1 - 3?

A

There are 3 values in the interval 1 - 3.

67
Q

How is the median interpreted in relation to data types?

A

The median is suitable for ordinal data and can also be used for interval and ratio data. It is less sensitive to extreme values compared to the mean.

68
Q

Define the advantages of using the median in data analysis.

A

The median is good for open-ended distributions, is not affected by missing or incomplete data, and provides a better measure of central tendency when the exact limits of the distribution are unknown.

69
Q

Explain the limitations of using the mean in certain data scenarios.

A

The mean can be sensitive to extreme values and may not accurately represent the central tendency if there are missing data points or if the distribution is open-ended.

70
Q

How does the median handle missing data in a dataset?

A

The median is not sensitive to missing scores in an open-ended distribution, making it a more reliable measure when data points are incomplete.

71
Q

Describe a scenario where the median would be preferred over the mean.

A

In a study where 100 rats are timed running through a maze, if 12 rats do not complete the maze, using the median would be preferred to avoid excluding the slower times of those rats, which could skew the mean.

72
Q

What is the significance of the median in open-ended distributions?

A

The median provides a central value that is not influenced by the extreme values or missing data points, making it a robust measure of central tendency in open-ended distributions.

73
Q

How does the median compare to the mean in terms of sensitivity to data points?

A

The median is less sensitive to extreme values and missing data points compared to the mean, which can be significantly affected by outliers.

74
Q

Describe the relationship between mean, median, and mode in a distribution where mean < median < mode.

A

In this distribution, the mean is the smallest value, followed by the median, and the mode is the largest value.

75
Q

Define the relationship between mean, median, and mode when mean = median = mode.

A

In this case, all three measures of central tendency are equal, indicating a perfectly symmetrical distribution.

76
Q

What does it mean if mode < median < mean in a distribution?

A

This indicates a positively skewed distribution where the tail on the right side is longer or fatter than the left side.

77
Q

How does the mean of a grouped frequency distribution compare to the mean of raw data?

A

The mean of a grouped frequency distribution may not equal the mean of the raw data.

PSYCH 211/D (9 decks)

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