i-Ready Practice Quiz: Center & Variability Answers

The mean is influenced by every value in the dataset, including extreme values or outliers. In contrast, measures like the median and mode are more resistant to such extremes.

The median is the middle value of a dataset when it is arranged in order. It effectively splits the data into two equal halves and is less affected by extreme values.

The mode identifies the most common or frequently occurring value in a dataset. This measure is particularly useful for categorical data where numerical averages are not meaningful.

The interquartile range (IQR) measures the spread of the central 50% of the data by calculating the difference between the third and first quartiles. It minimizes the effect of outliers by focusing on the middle portion of the dataset.

The range is calculated by subtracting the minimum value from the maximum value in a dataset. Although it provides a quick measure of spread, it can be heavily influenced by outliers.

To find the mean, add all values together: 4 + 8 + 6 + 5 + 3 = 26, then divide by the number of data points, 5, which yields 5.2. This is the average of the dataset.

The mode is the number that appears most frequently in a dataset. In this case, the number 3 appears twice while the others appear only once, making 3 the mode.

When the dataset is ordered, the median is the middle value, which in this case is 7. This value splits the dataset into two halves with an equal number of data points.

A low standard deviation means that most of the data points lie close to the mean. This indicates that there is relatively little variability in the dataset.

The median is less affected by extreme values compared to the mean, making it a more robust measure of central tendency in the presence of outliers. It offers a better representation of a typical value in skewed distributions.

When all values in a dataset are identical, there is no variation among them. This means that the standard deviation, which measures dispersion around the mean, is 0.

Standard deviation is defined as the square root of the variance, converting the squared units back to the original units of measurement. This makes the standard deviation easier to interpret in context.

When a constant is added to every value in the dataset, the entire set shifts by that constant but the differences between the minimum and maximum remain unchanged. Therefore, the range stays the same.

A larger variance indicates that data points are more spread out from the mean, showing greater dispersion. This measure captures how much the values in a dataset vary from the average.

Variance is calculated by taking the average of the squared differences from the mean, which means it considers every single deviation. This makes it highly sensitive to differences across the entire dataset.

Multiplying every observation in a dataset by a constant multiplies the standard deviation by the absolute value of that constant. Therefore, 5 multiplied by 3 gives a new standard deviation of 15.

The variance is calculated by averaging the squared differences from the mean, and the standard deviation is the square root of this variance. This relationship ensures that the standard deviation is in the same units as the original data.

A large difference between the mean and median typically suggests that the dataset is skewed due to the presence of outliers or extreme values. In such cases, the mean is pulled toward the tail of the distribution while the median remains more centrally located.

A high range indicates a greater difference between the smallest and largest values in the dataset, which usually corresponds to a higher overall spread. Consequently, the dataset with a high range is more likely to have a higher standard deviation.

The interquartile range (IQR) focuses on the middle 50% of the data and is not influenced by extreme values or outliers. Thus, it offers a more robust estimate of variability when outliers are present compared to measures that use all data points.