In a Box and Whisker plot, if the median line is closer to the left of the box then distribution will be: STA301

In a Box and Whisker plot, if the median line (which represents the second quartile, or Q2) is closer to the left of the box, it indicates that the data is positively skewed (also known as right-skewed).

This means:

• The majority of the data points are concentrated on the lower end of the range.
• There is a longer tail towards the higher values (right side of the distribution).
• The right side of the box (between Q2 and Q3) is wider than the left side (between Q1 and Q2), indicating that the upper half of the data is more spread out.

Thus, the distribution will be positively skewed.

When a coin is tossed, then sample space consists of: STA301

Yes, when a coin is tossed, the sample space consists of 2 possible outcomes.

The sample space represents all the possible outcomes of an experiment. For a single coin toss, the possible outcomes are:


S = {\text{Heads (H)}, \text{Tails (T)}}

So, the sample space has 2 outcomes: Heads and Tails. Hence, the number of elements in the sample space is 2.

One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?

3/13

A deck of 52 cards contains 12 face cards (Jack, Queen, and King from each of the four suits: hearts, diamonds, clubs, and spades).

The probability of drawing a face card is calculated as follows:



Here:

• The number of favorable outcomes (face cards) = 12
• The total number of outcomes (total cards in the deck) = 52

So, the probability is:

12/52= 3/13

Thus, the probability of drawing a face card is 3/13, which is correct!

The mean of a distribution is 24, the mode is 25 and the standard deviation is 5, then the coefficient of skewness will be: STA301

To calculate the coefficient of skewness using the given values, we can apply Pearson’s first coefficient of skewness formula:



Given:

• Mean = 24
• Mode = 25
• Standard Deviation = 5

Now, substitute the values into the formula:



So, the coefficient of skewness is -0.6. This indicates a slight negative skew in the distribution.

Since the coefficient of skewness we calculated is -0.6, it is less than zero, not greater than zero.

A negative skewness (less than zero) means that the distribution has a longer tail on the left side, and the mean is less than the mode. In this case, the mean (24) is indeed slightly less than the mode (25), which aligns with the negative skew.

If the skewness were greater than zero, it would indicate a positive skew, meaning the distribution’s tail is longer on the right, and the mean would be greater than the mode.

3/13