The mean of a dataset is calculated as ___?

The mean is calculated as the sum of all observations divided by the number of observations, represented as x = (Σxᵢ) / n.

True or False: The median of a dataset is affected by extreme values (outliers).

False. The median is the middle value of a dataset and is unaffected by extreme values. It provides a better measure of central tendency in skewed distributions.

Fill in the blank: The mode of a dataset is defined as the value that occurs ___ most frequently.

The mode of a dataset is defined as the value that occurs most frequently.

What is the formula for variance for ungrouped data?

The variance for ungrouped data is given by σ² = (Σ(xᵢ - x̄)²) / n, where x̄ is the mean and xᵢ are the individual data points.

True or False: The standard deviation is the square root of the variance.

True. The standard deviation is defined as σ = √(variance), which quantifies the dispersion in a dataset.

If the mean of a dataset is increased by a constant value a, what happens to the median?

If the mean is increased by a constant value a, the median will also increase by the same value a, as both are measures of central tendency.

Fill in the blank: The coefficient of variation is defined as the ratio of the standard deviation to the ___.

The coefficient of variation is defined as the ratio of the standard deviation to the mean, usually expressed as a percentage.

What does a higher standard deviation indicate about a dataset?

A higher standard deviation indicates greater variability or dispersion of the dataset values around the mean.

True or False: The mean and median of a symmetrical distribution are always equal.

True. In a symmetrical distribution, the mean, median, and mode coincide at the center of the distribution.

What is the relationship between mean, median, and mode in a moderately skewed distribution?

In a moderately skewed distribution, the relationship can be expressed as mode = 3 median - 2 mean.

Fill in the blank: The formula for combined mean of two datasets with means x₁ and x₂ is ___ where n₁ and n₂ are the sizes of the datasets.

The formula for combined mean is x̄ = (n₁x₁ + n₂x₂) / (n₁ + n₂).

What is the formula for the mean deviation about the mean?

The mean deviation about the mean is given by M.D. = (Σ|xᵢ - x̄|) / n, where x̄ is the mean and xᵢ are the individual data points.

True or False: The mode can be easily determined from a frequency distribution table.

True. The mode corresponds to the class or value with the highest frequency and can be easily identified from a frequency distribution.

Fill in the blank: In a continuous series, to find the median, the first step is to prepare a ___ frequency table.

In a continuous series, to find the median, the first step is to prepare a cumulative frequency table.

What is the formula for the standard deviation of a grouped dataset?

The standard deviation for a grouped dataset is given by σ = √(Σf(yᵢ - ȳ)²) / Σf, where ȳ is the mean and f is the frequency of each class.