The Captain of a Cricket team of 11 members is 26 years old and the Wicket keeper is 3 years older. If the ages of these two are excluded, The average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team? 

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Step into the cricket world with a 26-year-old captain and his 29-year-old wicketkeeper in a team of 11. Challenge yourself with the math puzzle: if we leave out their ages, the average age of the remaining players is one year less than the total team average. What’s the average age of the team?

The Captain of a Cricket team of 11 members is 26 years old and the Wicket keeper is 3 years older. If the ages of these two are excluded, The average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

Let’s call the average age of the entire team (including the captain and wicket-keeper) x. We can then set up two equations based on the information given:

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1. Average age with captain and wicket-keeper: x = (total age of all players) / 11
2. Average age without captain and wicket-keeper: x – 1 = (total age of remaining players) / 9

We know the ages of the captain and wicket-keeper, and we can also express the total age of the remaining players in terms of x:

• Total age of remaining players = (Total age of all players) – (Captain’s age + Wicket-keeper’s age) = 11x – (26 + 29) = 11x – 55

Now, we can substitute this expression for the total age of remaining players in the second equation:

x – 1 = (11x – 55) / 9

Multiplying both sides by 9:

9x – 9 = 11x – 55

Solving for x:

2x = 46

x = 23

Therefore, the average age of the entire team (including the captain and wicket-keeper) is 23 years old.

Significance of Averages in Mathematics

Averages, also known as measures of central tendency, are fundamental concepts in mathematics and statistics. They provide a way to summarize and describe a set of data points by identifying a representative or central value. The three main types of averages are the mean, median, and mode.

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1. Mean (Arithmetic Average):

   • The mean is calculated by adding up all the values in a data set and dividing the sum by the number of values.
   • It is the most common measure of central tendency.
   • The mean is sensitive to extreme values, often referred to as outliers.

2. Median:

   • The median is the middle value of a sorted data set.
   • It is less affected by extreme values compared to the mean, making it a more robust measure in the presence of outliers.
   • In an odd-sized dataset, the median is the middle value. In an even-sized dataset, it is the average of the two middle values.

3. Mode:

   • The mode is the value that appears most frequently in a data set.
   • A dataset may have one mode (unimodal), more than one mode (multimodal), or no mode at all.
   • The mode is particularly useful for categorical data.

Significance of Averages:

1. Central Tendency:

   • Averages provide a central or typical value around which data points cluster.
   • They help to summarize large amounts of data into a single representative value.

2. Comparisons:

   • Averages facilitate comparisons between different datasets or groups.
   • When comparing datasets, the one with a higher mean is generally considered to have higher overall values.

3. Predictions:

   • Averages are often used to make predictions and estimate future values.
   • For example, the mean is used to forecast trends or project future outcomes.

4. Data Interpretation:

   • Averages help in interpreting data by providing a simple summary.
   • They offer insights into the typical behavior or characteristics of a dataset.

5. Statistical Analysis:

   • Averages are essential in statistical analyses, such as hypothesis testing and regression analysis.
   • They serve as key parameters for many statistical models.

It’s important to note that while averages provide valuable insights, they may not capture the entire complexity of a dataset.

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Categories: Math