LECTURE 2 & 3

Which of the following is a measure of central tendency?

• Range

• Variance

• Median

• Standard deviation

Answer explanation

The median is a measure of central tendency that represents the middle value in a dataset when it is sorted in ascending or descending order. It is not affected by extreme values and provides a better representation of the center than the mean in skewed distributions

Which of the following measures provides information about the spread or variability of a dataset?

• Mean

• Median

• Mode

• Variance

Answer explanation

Variance is a measure of dispersion that calculates the average squared deviation from the mean. It indicates how spread out the values in a dataset are around the mean. A higher variance implies greater variability.

The range is a measure of:

• central tendency

• dispersion

• skewness

• kurtosis

Answer explanation

The range is a measure of dispersion that represents the difference between the maximum and minimum values in a dataset. It provides a simple measure of how spread out the data points are.

Which measure of central tendency is affected by the order of data values?

• Mean

• Median

• Mode

• Variance

Answer explanation

The median is the measure of central tendency that is affected by the order of data values. It represents the middle value when the data is sorted, so changing the order of values can alter its value.

What is the mean of the following numbers: 23, 45, 87, 40, 50?

• 49

• 34

• 56

• 78

What is the formula for calculating the mean of a set of data?

• Mean = sum of data values/ number of data values

• mean = median + mode

• Mean = largest data value - smallest data value

• Mean = standard deviation/range

The data set {3, 5, 7, 5, 9} has a mode of:

• 3

• 5

• 7

• 9

What is the formula for calculating the population standard deviation?

• √((Σ(x - μ)²) / (N - 1))

• √((Σ(x - μ)²) / N)

• √((Σ(x - μ)²) / (N + 1))

• √((Σ(x - μ)²) / (N * 2))

Answer explanation

The formula for calculating the population standard deviation is the square root of the sum of squared deviations from the population mean, divided by the number of data points (N). It is represented as: σ = √((Σ(x - μ)²) / N)

where:

σ (sigma) is the population standard deviation,

x is each individual data point,

μ (mu) is the population mean, and

N is the number of data points in the population.

What is the formula for calculating the sample standard deviation?

• √((Σ(x - x̄)²) / N)

• √((Σ(x - x̄)²) / (N + 1))

• √((Σ(x - x̄)²) / (N - 1))

• √((Σ(x - x̄)²) / (N * 2))

Answer explanation

The formula for calculating the sample standard deviation is similar to the population standard deviation, except for the denominator. It is the square root of the sum of squared deviations from the sample mean, divided by the number of data points minus one (N - 1). The formula is represented as: s = √((Σ(x - x̄)²) / (N - 1))

where:

s is the sample standard deviation,

x is each individual data point,

x̄ (x-bar) is the sample mean, and

N is the number of data points in the sample.

A fair six-sided dice is rolled. What is the probability of rolling an odd number?

• 1/6

• 1/3

• 1/2

• 2/3

Answer explanation

A fair six-sided dice has six equally likely outcomes: {1, 2, 3, 4, 5, 6}. Out of these outcomes, three numbers (1, 3, and 5) are odd. Therefore, the probability of rolling an odd number is 3/6 or 1/2