Probability and Statistics – Solved Examples
Example 1: Consider the following dataset: [5, 8, 2, 5, 3, 7, 9]. Calculate the mean, median, and mode.
Solution:
Mean =
= [5+8+2+5+3+7+9] / 7
⇒ 39/7 = 5.579
Median:
The number of values in data set is 7, which is odd nby arranging the values in ascending order [2, 3, 5, 5, 7, 8, 9].
The median is the 4th value, which is 5.
Mode: The mode is 5, as it appears more frequently than any other number in the dataset.
Example 2: Given the dataset [12, 15, 18, 22, 25], calculate the variance and standard deviation.
Solution:
The given data set is [12, 15, 18, 22, 25]
Mean =
⇒ = sum of all values / total number of values
⇒ = (12+15+18+22+25) / 5
⇒ 92/5
⇒ 18.4
Now,
Variance = Variance= ∑(Each value−Mean) 2 / Total number of values
⇒ σ2 = [(12−18.4)2 + (15−18.4)2 + (18−18.4)2 + (22−18.4)2 + (25−18.4)2 ] / 5
⇒ [41.64 + 11.56 + 0.16 + 13.44 + 43.56] /5
⇒ 110.36 /5
⇒ 22.072
We know,
Standard deviation = √σ2
⇒ √22.072
√σ2= 4.69
Example 3: In a deck of cards, what is the probability of drawing a red card?
Solution:
Total number of cards in a deck = 52
Total number od Red cards in a deck = 26 (hearts + diamonds)
P(Red Card) = 52/26
⇒ P(Red Card) = 2/4
⇒ P (Red Card) = 1/2 or 0.5 or 50%
Probability and Statistics
Probability and Statistics are helpful guides when it comes to studying numbers. Probability helps us figure out how likely things are to happen, like guessing if it will rain. On the other hand, Statistics is about collecting and understanding data, like looking at numbers to learn useful things. Together, they help us make smart decisions and see patterns in the information around us.
This article covers various concepts of probability and statistics. In probability, we will learn definitions, formulas, types of events, Rules of probability, and more topics related to probability.
Table of Content
- What is Probability And Statistics?
- Probability Definition
- Statistics Definition
- Terms Related to Probability and Statistics
- Probability and Statistics Formulas
- Probability Formulas
- Statistics Formulas
- Topics under Probability and Statistics
- Rules of Probability
- Types of Event in Probability
- Statistics Topics
- Probability and Statistics for Engineering Mathematics
- Probability in Engineering
- Statistics in Engineering
- Probability and Statistics – Solved Examples
- Practice Problems on Probability and Statistics
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