Statistics and Probability

What is the formula to calculate mean deviation from the mean?

• Mean deviation from the mean = Σ(X - μ) / n

• Mean deviation from the mean = Σ|X - μ| * n

• Mean deviation from the mean = Σ(X - μ) - n

• Mean deviation from the mean = Σ|X - μ| / n, where X is each data point, μ is the mean, and n is the total number of data points.

How is variance calculated in statistics?

• Variance is calculated by finding the median of the data set

• Variance is calculated by taking the average of the squared differences between each data point and the mean of the data set.

• Variance is calculated by taking the square root of the sum of the data points

• Variance is calculated by dividing the sum of the data points by the number of data points

Define standard deviation and explain its importance in data analysis.

• Standard deviation is a measure of the amount of variation or dispersion of a set of values. It shows how much the values differ from the mean. In data analysis, standard deviation helps in understanding the spread of data points around the mean and identifying outliers.

• Standard deviation is calculated by dividing the range of data by the number of data points.

• Standard deviation is a measure of central tendency in data analysis.

• Standard deviation is used to identify the maximum value in a dataset.

If the probability of an event A is 0.3, what is the probability of the complement of A?

• 0.2

• 0.7

• 0.5

• 0.8

A fair six-sided dice is rolled. What is the probability of rolling a 3?

• 1/3

• 1/4

• 1/5

• 1/6

In a deck of 52 cards, what is the probability of drawing a red card?

• 0.75

• 0.25

• 0.5

• 1.0

Explain the concept of mutually exclusive events in probability.

• Mutually exclusive events are events that have no outcomes in common. If one event occurs, the other event cannot occur.

• Mutually exclusive events are events that are completely unrelated.

• Mutually exclusive events are events that have all outcomes in common.

• Mutually exclusive events are events that always occur together.

Calculate the mean deviation from the mean for the following data set: 5, 8, 10, 12, 15

• 1.5

• 3.2

• 2.8

• 4.7

If the variance of a data set is 16, what is the standard deviation?

• 4

• 12

• 8

• 2

Two events A and B are independent. If the probability of A is 0.4 and the probability of B is 0.3, what is the probability of both events occurring?

• 0.25

• 0.07

• 0.12

• 0.35