Ap Statistics Chapter 1

1. What is the mean?

The mode; the number that appears most frequently in a set of numbers.

The median; the middle value in a set of numbers.

The range; the difference between the largest and smallest values in a set of numbers.

The average; most common measure of centrality; not resistant.

The mean is calculated by adding up all the values in a set and dividing by the number of values. It is the most commonly used measure of centrality, but is not resistant to outliers.

Explanation

The mean is calculated by adding up all the values in a set and dividing by the number of values. It is the most commonly used measure of centrality, but is not resistant to outliers.

2. What do quartiles represent in a dataset?

Represents the highest values in the dataset.

Indicates the total range of the data values.

Shows spread of the middle half of the data.Q1(lower quartile): cuts off lowest 25% of data; 25th percentile; median of the lower half of the data.Q3(upper quartile): cuts off lowest 75%; 75th percentile; median of the upper half of the data. Example: [3, 6, 7, 7, 8, 8, 9, 10, 12, 12, 15]Q1=7 Q3=12

Divides the dataset into ten equal parts.

Quartiles divide a dataset into four equal parts to show the spread of the middle half of the data. Q1 represents the 25th percentile, cutting off the lowest 25% of data, and Q3 represents the 75th percentile, cutting off the lowest 75% of data.

Explanation

Quartiles divide a dataset into four equal parts to show the spread of the middle half of the data. Q1 represents the 25th percentile, cutting off the lowest 25% of data, and Q3 represents the 75th percentile, cutting off the lowest 75% of data.

3. What does Interquartile Range (IQR) measure?

The maximum value in a data set.

The average value of a data set.

The total range of a data set.

The best measure for finding outliers; the middle 50% of a data set.Formula: Q3-Q1

Interquartile Range (IQR) is specifically designed to measure the spread and variability within the middle 50% of a data set, making it effective for identifying outliers while discounting extreme values.

Explanation

Interquartile Range (IQR) is specifically designed to measure the spread and variability within the middle 50% of a data set, making it effective for identifying outliers while discounting extreme values.

4. What is an outlier?

A point that falls outside the IQR - maximum value, or the IQR + minimum value.

A point that falls within the IQR - maximum value and the IQR + minimum value.

A point that falls outside the IQR x 1.5 + maximum value, or the IQR x 1.5 - minimum value. Example of finding outliers: [3, 6, 7, 7, 8, 8, 9, 10, 12, 12, 15](Q3-Q1): 12-7=5(formula for finding outliers)1.5 x 5= 7.515(maximum)+7.5=22.5(upper outlier minimum)3(minimum) - 7.5=-4.5(lower outlier maximum)

A point that falls within the IQR x 1.5 + maximum value and the IQR x 1.5 - minimum value.

An outlier is a point that lies beyond a certain range calculated based on the Interquartile Range (IQR) and 1.5 times the IQR value from the upper or lower quartile.

Explanation

An outlier is a point that lies beyond a certain range calculated based on the Interquartile Range (IQR) and 1.5 times the IQR value from the upper or lower quartile.

5. What does the term 'Five Number Summary' represent?

A summary of the arithmetic mean, mode, and range of a data set.

A summary of five random numbers from a data set.

Has a data set's minimum value, lower quartile, median, upper quartile, maximum value; itself can create a boxplot.

A summary of the top five values in a data set.

The Five Number Summary represents specific values within a data set that include the minimum, lower quartile, median, upper quartile, and maximum value. It is used to create a boxplot to visually represent the distribution of data.

Explanation

The Five Number Summary represents specific values within a data set that include the minimum, lower quartile, median, upper quartile, and maximum value. It is used to create a boxplot to visually represent the distribution of data.

6. What is a Boxplot (Modified)?

A graph that uses the five number summary.

A visualization technique that only shows the mean and median

A type of line graph

A type of scatter plot that uses two variables

A Boxplot (Modified) is a graph that displays the five number summary which includes the minimum, first quartile, median, third quartile, and maximum of a dataset. It is used to visually represent the distribution and skewness of the data.

Explanation

A Boxplot (Modified) is a graph that displays the five number summary which includes the minimum, first quartile, median, third quartile, and maximum of a dataset. It is used to visually represent the distribution and skewness of the data.

7. What is Variance?

Standard Deviation; a measure of the dispersion of a set of values from the mean.

Mean Absolute Deviation; the average of the absolute differences between values and the mean.

Range; the difference between the highest and lowest values in a dataset.

S2; the average of the squares of the deviations of values from the mean

Variance measures how spread out the values in a data set are from the mean, by calculating the average of the squared differences between each data point and the mean. It is commonly denoted as s2 in statistics.

Explanation

Variance measures how spread out the values in a data set are from the mean, by calculating the average of the squared differences between each data point and the mean. It is commonly denoted as s2 in statistics.

8. What does the Standard Deviation measure?

Measures the spread by seeing how far the values are from the mean; the square root of the variance; not resistant; should only be used if the mean of a data set is chosen as its measure of centrality.

Measures the central tendency of a dataset

Measures the lowest value in a dataset

Measures the highest value in a dataset

Standard deviation is a measure of the dispersion or spread of a set of values around the mean. It is the square root of the variance and is not resistant to outliers. It is best used when the mean is chosen as the measure of centrality for the data set.

Explanation

Standard deviation is a measure of the dispersion or spread of a set of values around the mean. It is the square root of the variance and is not resistant to outliers. It is best used when the mean is chosen as the measure of centrality for the data set.

9. When can back-to-back stemplots be used effectively?

Best for comparing spreads of data sets

Not useful in comparing any quantitative values

Good for comparing the shapes of 2 data sets or small numbers of quantitative values, but for comparing the centers or the spreads, a side-by-side boxplot would be better. They both are effective in comparing quantitative distributions. Example (with picture): City 1[32, 43, 48, 56, 69] City 2[38, 41, 51, 57, 64]

Ideal for comparing centers of data sets

Back-to-back stemplots are useful for comparing the shapes of data sets or small numbers of quantitative values, while side-by-side boxplots are better for comparing centers or spreads. Each method has its own strengths in comparing quantitative distributions.

Explanation

Back-to-back stemplots are useful for comparing the shapes of data sets or small numbers of quantitative values, while side-by-side boxplots are better for comparing centers or spreads. Each method has its own strengths in comparing quantitative distributions.