Explanation

When flipping a coin 3 times, each flip has 2 possible outcomes (heads or tails).

So, the total number of outcomes is 2³ = 8.

The favorable outcome is getting 3 heads (HHH).

There is only 1 way to achieve this.

Probability = Number of favorable outcomes / Total number of outcomes = 1/8 = 0.125.

Explanation

Range is the simplest measure of data spread, calculated by subtracting the smallest value from the largest value.

It gives an idea of how widely the data values are spread.

Explanation

Each die has 6 faces, so the total outcomes when rolling two dice = 6 × 6 = 36.

Only 1 outcome gives 5 on both dice: (5,5). So, probability = 1/36.

Explanation

Temperature is continuous data because it can take any value within a range (e.g., 30.5°C, 30.55°C).

Continuous data can be measured on a scale, not just counted.

Explanation

Step 1: Calculate the mean of the marks.

Mean = (6 + 8 + 10 + 12 + 4 + 20) / 6

= 60 / 6

= 10

Step 2: Calculate the mean deviation.

Mean Deviation = (|6-10| + |8-10| + |10-10| + |12-10| + |4-10| + |20-10|) / 6

= (4 + 2 + 0 + 2 + 6 + 10) / 6

= 24 / 6

= 4

Step 3: Calculate the coefficient of dispersion.

Coefficient of Dispersion = Mean Deviation / Mean

= 4 / 10

= 0.4

Explanation

The standard deviation of a binomial distribution is indeed √npq, where:

• n is the number of trials
• p is the probability of success
• q is the probability of failure (q = 1 - p)

The formula for the standard deviation of a binomial distribution is:

σ = √npq

This represents the spread or dispersion of the distribution.

Explanation

Geometric Mean = ∛(2 × 4 × 8)

= ∛64

= 4

Explanation

A bimodal distribution has two modes, meaning two values occur with the highest and equal frequency.

It indicates the presence of two peaks in the data set.

Explanation

A small standard deviation means the data is tightly clustered around the mean.

This results in a less spread out (narrower) normal distribution curve.

Explanation

Mode is the value that occurs most frequently in a dataset.

It represents the most common or popular item in the data.