## Questions and Answers

What does the minimum value of a set of data show?

The smallest value in the data

What does the kth largest value represent in a set of data?

The highest kth number of the data

What can be inferred from a positively skewed distribution?

Most of the data are clustered to the left side of the distribution

What does a kurtosis of -1.36 indicate about a distribution?

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What does the count of a set of data show?

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What percentage of scores will be eliminated from the reaction time data if the researcher believes that scores farthest from the mean are due to error?

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What is the mean of the reaction time data?

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What is the standard deviation of the reaction time data?

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What percentage of scores fall between the raw scores of 76 and 93 in the set of scores with a mean of 89 and a standard deviation of 12?

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What is the lowest grade a person could receive and still get into the accelerated math class?

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What is the average number of hours that Senior High School students spend sleeping in a week?

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At what time have half of the students finished the exam?

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What is the percentage of students who have finished the exam at 35 minutes?

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What is the purpose of descriptive statistics in the context of the reaction time data?

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What is the purpose of descriptive statistics in the context of the sleep data?

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## Study Notes

### Descriptive Statistics for Quantitative Data

- Descriptive statistics is a way to summarize and describe a data set using brief descriptive coefficients.
- It is used to provide a visual summary of data.
- Prior to gathering data, it is essential to identify the level of measurement of the quantitative data and determine the kind of descriptive statistics to be performed.

### Measures of Central Tendency

- Measures of central tendency describe the center position of a distribution for a data set.
- The three types of measures of central tendency are:
- Mean: the average of the numbers, used if the level of measurement is interval or ratio.
- Median: the middle value of the data, used if the level of measurement is ordinal.
- Mode: the data that appears most often, used if the level of measurement is nominal.

### Measures of Variability

- Measures of variability describe the spread of scores in a set of data.
- The three types of measures of variability are:
- Standard deviation: represents the measure of how spread out the scores are, and can be obtained using the formula: σ = √(Σ(X-μ)^2 / N)
- Sample variance: shows how varied a sample is, and is the square of the standard deviation.
- Range: the difference between the highest and lowest score of the data.

### Distribution of the Data

- Skewness refers to the distortion or asymmetry in a symmetrical bell curve.
- Kurtosis refers to the sharpness of the peak of a distribution.
- A distribution can be:
- Positively skewed: most of the data are clustered to the left side of the distribution.
- Negatively skewed: most of the data are clustered to the right side of the distribution.
- Moderately skewed: skewness is between -1 and -0.5 or between 0.5 and 1.
- Approximately symmetric: skewness is between -0.5 and 0.5.
- Perfectly symmetrical: skewness is 0.
- Mesokurtic: kurtosis is between -1 and 1.
- Leptokurtic: kurtosis is greater than 1.
- Platykurtic: kurtosis is less than -1.

### Other Descriptive Statistics

- Minimum value: the smallest value in a set of data.
- Maximum value: the largest value in a set of data.
- Sum: the value when all the values of the data are added.
- Count: the number of data.
- Kth largest value: the highest kth number of the data.
- Kth smallest value: the lowest kth number of the data.
- Confidence level: the suitable interval above and below the mean to estimate the population mean with a specified confidence level.

### Using Microsoft Excel for Descriptive Statistics

- To perform descriptive statistics in Microsoft Excel, follow these steps:
- Enter the data on the spreadsheet.
- Under the Data ribbon, click "Data Analysis."
- Click "Descriptive Statistics" and press "OK."
- Under the input range, highlight the cells that contain the data.
- Tick the checkbox under "Summary statistics" and set it to 95%.
- Tick the checkboxes under Confidence Level of the Mean, Kth Largest, and Kth Smallest.
- Press "OK."

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