Explanation

1. Arrange Data in Ascending Order:

   $$\mathrm{<b><font\; color="\#0000ff">2.5</font></b>}<b><font\; color="\#0000ff">,</font></b>\mathrm{<b><font\; color="\#0000ff">2.8</font></b>}<b><font\; color="\#0000ff">,</font></b>\mathrm{<b><font\; color="\#0000ff">2.8</font></b>}<b><font\; color="\#0000ff">,</font></b>\mathrm{<b><font\; color="\#0000ff">2.9</font></b>}<b><font\; color="\#0000ff">,</font></b>\mathrm{<b><font\; color="\#0000ff">3.0</font></b>}<b><font\; color="\#0000ff">,</font></b>\mathrm{<b><font\; color="\#0000ff">3.3</font></b>}<b><font\; color="\#0000ff">,</font></b>\mathrm{<b><font\; color="\#0000ff">3.4</font></b>}<b><font\; color="\#0000ff">,</font></b>\mathrm{<b><font\; color="\#0000ff">3.6</font></b>}<b><font\; color="\#0000ff">,</font></b>\mathrm{<b><font\; color="\#0000ff">3.7</font></b>}<b><font\; color="\#0000ff">,</font></b>\mathrm{<b><font\; color="\#0000ff">4.0</font></b>}<b><font\; color="\#0000ff">,</font></b>\mathrm{<b><font\; color="\#0000ff">4.4</font></b>}<b><font\; color="\#0000ff">,</font></b>\mathrm{<b><font\; color="\#0000ff">4.8</font></b>}<b><font\; color="\#0000ff">,</font></b>\mathrm{<b><font\; color="\#0000ff">4.8</font></b>}<b><font\; color="\#0000ff">,</font></b>\mathrm{<b><font\; color="\#0000ff">5.2</font></b>}<b><font\; color="\#0000ff">,</font></b>\mathrm{<b><font\; color="\#0000ff">5.6</font></b>}$$

2. Find Median:

   • There are 15 data points (odd number), so the median is the 8th value in the ordered list.

   • The 8th value is 3.6.

Explanation

Explanation

Explanation

A trade surplus occurs when a country exports more goods and services than it imports.

This indicates a positive balance of trade, where the country earns more revenue from exports than it spends on imports.

Explanation

The most frequent or curing value in a data set is called the Mode.

Mode is the value that appears most often in the data set.

Explanation

If the bag contains 5 red bags and 3 blue bags, the total number of bags is:

$$5 + 3 = 8$$

The probability of selecting a red bag is:

$$P(text{Red bag}) = frac{text{Number of red bags}}{text{Total number of bags}} = frac{5}{8}$$

So, the probability is $frac{5}{8}$, which equals 0.625 or 62.5%.

Explanation

Total number of cards: 12

(i) Probability of drawing '8'

• Favorable outcomes: 1 (card number 8)
• Probability: 1/12

(ii) Probability of drawing an even number

• Favorable outcomes: 6 (2, 4, 6, 8, 10, 12)
• Probability: 6/12 = 1/2

(iii) Probability of drawing a perfect square

• Favorable outcomes: 4 (1, 4, 9)
• Probability: 4/12 = 1/3

(iv) Probability of drawing a negative number

• Favorable outcomes: 0 (no negative numbers)
• Probability: 0/12 = 0

(v) Probability of drawing a number less than 13

• Favorable outcomes: 12 (all cards are less than 13)
• Probability: 12/12 = 1

In summary:

• Probability of drawing '8': 1/12
• Probability of drawing an even number: 1/2
• Probability of drawing a perfect square: 1/3
• Probability of drawing a negative number: 0
• Probability of drawing a number less than 13: 1

Explanation

The mean of 5 observations is 10.

This means the sum of the 5 observations is:

$$\text{Sum of 5 observations}=\text{Mean}\times \text{Number of observations}=10\times 5=50$$

Now, a new observation (10) is added. The new sum becomes:

$$\text{New sum}=50+10=60$$

The new mean of the 6 observations is:

New mean=New sum/Number of observations

​=660​

=10

Explanation

The range of probability for each event lies between 0 and 1.

This means that the probability of any event can be a value from 0 (impossible event) to 1 (certain event).

Explanation

If we add a constant (such as 3) to each observation of a data set, the mean will be increased by 3

This is because adding the same constant to each data point shifts the entire data set by that constant value, including the mean.