Statistics Measures of Central Tendency

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Questions and Answers

What type of data is referred to as first-hand data gathered by the researcher?

Tertiary Data

Secondary Data

Qualitative Data

Primary Data (correct)

Which of the following is an example of a continuous variable?

Height of individuals (correct)

Car models

Favorite color

Number of students in a class

What distinguishes a qualitative variable from a quantitative variable?

Qualitative variables are always numerical.

Qualitative variables can be placed into distinct categories. (correct)

Qualitative variables can be ranked.

Qualitative variables can be measured.

Which level of measurement is used when numbering subjects for counting purposes only?

Nominal Signup and view all the answers

In which level of measurement are variables ranked but the intervals between ranks are not known?

Ordinal Signup and view all the answers

Which of the following best describes discrete variables?

They are based on counting. Signup and view all the answers

What type of data includes observations collected from online sources?

Secondary Data Signup and view all the answers

Which measurement level allows for the use of mathematical operations on numbers?

Interval Signup and view all the answers

What is the median of the following set of numbers: 3.3, 6.6, 3.0, 9.8, 3.7, 2.9, 5.5, 8.0?

4.6 Signup and view all the answers

Which statement about the median is true?

It is a measure of central tendency. Signup and view all the answers

Which type of mode refers to a distribution that has one mode?

Unimodal Signup and view all the answers

In which situation is the mode most useful?

When data are nominal. Signup and view all the answers

What does a high measure of dispersion indicate?

Data points are widely spread out. Signup and view all the answers

What represents the mode in the following dataset: 11, 14, 12, 11, 15, 16, 18, 11, 10, 17?

11 Signup and view all the answers

When is the median considered the best measure of central tendency?

Both B and C. Signup and view all the answers

If a given data set has no repeating values, what can be stated about its mode?

The mode is undefined. Signup and view all the answers

What is the formula for calculating the range of a data set?

R = H - L Signup and view all the answers

What does a small range indicate about a distribution of scores?

Scores are clustered and homogenous. Signup and view all the answers

Which of the following is considered the most reliable measure of variability?

Standard Deviation Signup and view all the answers

What is the first step in calculating the standard deviation?

Find the mean. Signup and view all the answers

In the standard deviation formula, what does N represent?

Total number of scores Signup and view all the answers

What does a large standard deviation indicate about a data set?

Data points are varying and spread apart. Signup and view all the answers

What is the formula used to calculate the z-score?

z = (score - mean) / sd Signup and view all the answers

What does kurtosis measure in a frequency-distribution curve?

The sharpness of the peak of the distribution. Signup and view all the answers

In which subject did June perform better relative to his classmates?

Calculus Signup and view all the answers

What is the relationship between variance and standard deviation?

Standard deviation is the square root of variance. Signup and view all the answers

What is the z-score for Ruda in Science?

1.0 Signup and view all the answers

Which subject corresponds to Ruda's lowest z-score?

Math Signup and view all the answers

What does a higher z-score indicate about a student's performance?

Performance is above average. Signup and view all the answers

If Ruda scored 30 in Math while the mean is 22 and the standard deviation is 7, what is his z-score in Math?

1.10 Signup and view all the answers

What is the relationship between average scores and z-scores?

Higher scores result in higher z-scores regardless of averages. Signup and view all the answers

Which subject had the highest calculated z-score for Ruda?

English Signup and view all the answers

What distinguishes a ratio scale from an interval scale?

Ratio scale has a true zero indicating absence of the characteristic. Signup and view all the answers

Which of the following is an example of an interval scale?

Temperature in Celsius Signup and view all the answers

For what type of data is the mean most appropriate as a measure of central tendency?

Interval or ratio data in a symmetrical distribution. Signup and view all the answers

What is the mean of the data set: 42, 47, 39, 57, 55, 31, 46, 24, 18, 23?

38.2 Signup and view all the answers

Which measure of central tendency is least affected by extreme scores?

Median Signup and view all the answers

What can be concluded about a data set where the mean is significantly higher than the median?

Data is positively skewed. Signup and view all the answers

What is the value of Timmy's average for the 1st quarter given the grades: English = 93, Math = 89, Science = 91, Values = 76?

87.25 Signup and view all the answers

Which attribute is uniquely characteristic of a ratio scale?

It allows for the comparison of absolute values. Signup and view all the answers

Study Notes

Measures of Central Tendency

Mean, median, and mode are single values used to represent the center of a dataset.
Mean, also known as arithmetic mean, is calculated by summing all values and dividing by the total number of values.
It's most stable and used to compare other measures like standard deviation and skewness.
Mean is affected by extreme values.
Median is the middlemost value when the data is arranged in order.
It is not influenced by extreme values, making it a reliable measure for skewed data.
Mode is the value that appears most frequently in a dataset.
It can be unimodal (one mode), bimodal (two modes), trimodal (three modes), or multimodal (more than two modes).
It is not affected by outliers and may not exist in some datasets.

Measures of Dispersion/Variability

Measures of dispersion indicate the spread or variability of data points around the central tendency.
A smaller dispersion signifies data points are close to the center, while a larger dispersion indicates data points are spread over a larger range.
Range is the difference between the highest and lowest values in a distribution.
It's sensitive to extreme values, making it less reliable than other measures.
Standard deviation (SD) is a commonly used and reliable measure of variability.
It represents the average deviation of data points from the mean.
A smaller SD implies data points are close to the mean, while a larger SD indicates greater spread.
Variance is the square of the standard deviation.
It measures the average squared deviations from the mean.

Z-score

The z-score indicates how many standard deviations a data point is away from the mean.
A positive z-score implies the data point is above the mean, while a negative z-score indicates it’s below the mean.

Types of Data

Data refers to raw, factual information used for analysis.
Primary data is collected firsthand by the researcher, such as national census data.
Secondary data is collected by others, such as data from online sources.
Population represents all individuals of interest in a study.
Sample is a subset of individuals selected from a population to represent the population in a study.

Types of Variables

Variables are characteristics that change or differ among individuals.
Qualitative variables are categorical and cannot be meaningfully ordered or ranked, such as gender.
Quantitative variables are measurable using a number scale, allowing for ranking or ordering, such as height.

Types of Quantitative Variables

Discrete variables are obtained by counting, such as the number of children.
Continuous variables are obtained by measuring, such as temperature.

Levels of Measurement

Nominal level is used for naming and categorization only and cannot be ordered or computed. Examples include gender, nationality, and civil status.
Ordinal level allows for ranking or ordering but doesn’t provide information about the size of difference between ranks. Examples include year level, level of satisfaction, and educational qualification.
Interval level represents values with known sizes or distances, but zero doesn’t indicate an absence of the characteristic. Examples include temperature in Celsius or Fahrenheit and test scores.
Ratio level possesses all characteristics of the interval scale and has a true zero point, indicating an absence of the characteristic. Examples include height, weight, age, and monetary savings.

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Description

Explore the key concepts of central tendency including mean, median, and mode. Understand how these measures represent data and their roles in data analysis. Learn about the impact of extreme values and discover the significance of measures of dispersion.