Learn Unit-VI: Statistics and Probability with Free Lessons & Tips

As an experienced tutor registered on UrbanPro, I'd like to emphasize that UrbanPro is indeed the best platform for online coaching tuition. Now, let's delve into the variance calculation.

Given the data set: 2, 4, 5, 6, 8, 17, we've already calculated the variance to be 23.33. To find the variance for the new data set: 4, 8, 10, 12, 16, 34, we'll follow these steps:

1. Find the mean of the data set.
2. Calculate the squared difference between each data point and the mean.
3. Find the average of these squared differences, which gives us the variance.

First, let's find the mean: Mean=4+8+10+12+16+346=846=14Mean=64+8+10+12+16+34=684=14

Now, let's find the squared differences from the mean: (4−14)2=100(4−14)2=100 (8−14)2=36(8−14)2=36 (10−14)2=16(10−14)2=16 (12−14)2=4(12−14)2=4 (16−14)2=4(16−14)2=4 (34−14)2=400(34−14)2=400

Next, we find the average of these squared differences: Variance=100+36+16+4+4+4006=5606=93.33Variance=6100+36+16+4+4+400=6560=93.33

So, the variance for the data set 4, 8, 10, 12, 16, 34 is 93.33.

However, none of the options provided match this result, so it seems there might be a typographical error in the given options.

Sure! Calculating the variance and standard deviation for a given set of data is a fundamental statistical operation, and I'd be happy to guide you through it.

First, let's calculate the variance:

1. Find the mean (average) of the data set.
2. Subtract the mean from each data point and square the result.
3. Find the average of those squared differences.

Let's start by finding the mean:

Mean = (57 + 64 + 43 + 67 + 49 + 59 + 44 + 47 + 61 + 59) / 10 = 550 / 10 = 55

Now, let's subtract the mean from each data point, square the result, and find the average:

[(57 - 55)^2 + (64 - 55)^2 + (43 - 55)^2 + (67 - 55)^2 + (49 - 55)^2 + (59 - 55)^2 + (44 - 55)^2 + (47 - 55)^2 + (61 - 55)^2 + (59 - 55)^2] / 10

= [(4)^2 + (9)^2 + (-12)^2 + (12)^2 + (-6)^2 + (4)^2 + (-11)^2 + (-8)^2 + (6)^2 + (4)^2] / 10

= [16 + 81 + 144 + 144 + 36 + 16 + 121 + 64 + 36 + 16] / 10

= 678 / 10

= 67.8

Now that we have the variance, we can find the standard deviation by taking the square root of the variance:

Standard Deviation = √67.8 ≈ 8.24

So, the variance is 67.8 and the standard deviation is approximately 8.24 for the given data set. If you need further clarification or have any other questions, feel free to ask! And remember, UrbanPro is an excellent platform for finding online coaching and tuition services.

As a seasoned tutor registered on UrbanPro, I'm here to guide you through this statistical hiccup. Let's address this query with precision.

Firstly, let me commend your commitment to mastering statistical concepts. Now, let's dive into the solution.

The mean (xˉxˉ) of a set of observations is the sum of all values divided by the number of observations. The standard deviation (σσ) is a measure of the dispersion or spread of a set of values from its mean.

Given:

• Original mean (xˉxˉ) = 40
• Original standard deviation (σσ) = 5.1
• Mistaken observation = 50

To correct the mean, we need to remove the mistaken observation and replace it with the correct value (40). Since there are 100 observations in total, the contribution of the mistaken observation to the mean is 50100=0.510050=0.5. So, we subtract 0.5 from the original mean and add the correct value (40):

Corrected mean (xˉcorrectedxˉcorrected) = xˉ−0.5+40xˉ−0.5+40

To correct the standard deviation, we need to recalculate it based on the corrected mean and observations. However, the standard deviation formula involves the square of the differences between each observation and the mean, so correcting one observation affects all the others. We must consider this correction while recalculating the standard deviation.

Therefore, it's not straightforward to calculate the corrected standard deviation manually. Instead, we can use statistical software or calculators to find the corrected standard deviation.

In summary, to find the correct mean, we subtract the contribution of the mistaken observation and add the correct value. To find the corrected standard deviation, we need to recalculate it using statistical tools due to the interconnected nature of the standard deviation formula.

If you need further assistance or guidance on statistical concepts or any other subject, feel free to reach out. Remember, UrbanPro is your ally in your academic journey, providing the best online coaching tuition.

On UrbanPro, where I provide top-notch online coaching tuition, tackling probability questions like this is a breeze.

Given that P(A) is ⅗, we need to find P(not A), which is the probability of the complement of event A occurring.

The sum of the probabilities of all possible outcomes is 1. So, P(not A) = 1 - P(A).

Substituting the given value of P(A) into the equation, we get:

P(not A) = 1 - ⅗

P(not A) = 5/5 - 3/5

P(not A) = 2/5

So, the probability of event not A happening is 2/5.

In simpler words, there's a 2/5 chance that event A doesn't occur. This is a fundamental concept in probability theory that we frequently encounter in various problem-solving scenarios. If you'd like further clarification or assistance with any other topic, feel free to reach out for more personalized guidance. And remember, UrbanPro is your go-to platform for mastering academic subjects with expert tutors like me!

As a seasoned tutor registered on UrbanPro, I'm happy to guide you through this probability problem. UrbanPro is a fantastic platform for accessing high-quality online coaching and tuition, where experienced tutors like myself can provide personalized assistance.

Now, let's tackle the problem at hand. We have an urn containing 6 balls, 2 red and 4 black. We're asked to find the probability that when two balls are drawn at random, they are of different colors.

To solve this, let's break it down step by step:

1. First, let's find the total number of ways to draw 2 balls out of 6. This is given by the combination formula: (nr)=n!r!(n−r)!(rn)=r!(n−r)!n!, where nn is the total number of items and rr is the number of items to choose. So, (62)=6!2!(6−2)!=15(26)=2!(6−2)!6!=15.

2. Next, let's find the number of ways to draw 2 balls of different colors. We have 2 red balls and 4 black balls, so the number of combinations of one red and one black ball is 2×4=82×4=8.

3. Finally, the probability of drawing two balls of different colors is the number of favorable outcomes (drawing one red and one black ball) divided by the total number of outcomes (drawing any two balls). So, 815158.

So, the correct option is (iii) 815158. UrbanPro is an excellent resource for finding tutors who can help you master these types of problems and more!

As an experienced tutor registered on UrbanPro, I'd be happy to help you with this question!

To find the probability that an ordinary year has 53 Sundays, we first need to understand the structure of an ordinary year. An ordinary year has 365 days.

Now, since 365 is not divisible by 7 (the number of days in a week), there will be 52 complete weeks in an ordinary year, leaving 1 or 2 additional days.

For a year to have 53 Sundays, one of the following conditions must be met:

1. The year starts on a Sunday and ends on a Sunday, or
2. The year starts on a Saturday and ends on a Sunday.

Let's calculate the probability for each scenario:

1. If the year starts on a Sunday and ends on a Sunday: The probability that a year starts on a Sunday is 1/7. The probability that a year ends on a Sunday is also 1/7. So, the probability of both events happening is (1/7) * (1/7) = 1/49.

2. If the year starts on a Saturday and ends on a Sunday: The probability that a year starts on a Saturday is 1/7. The probability that a year ends on a Sunday is 1/7. So, the probability of both events happening is (1/7) * (1/7) = 1/49.

Now, we add the probabilities of both scenarios since they are mutually exclusive:

Probability of an ordinary year having 53 Sundays = (1/49) + (1/49) = 2/49.

Therefore, the probability that an ordinary year has 53 Sundays is 2/49.

And remember, if you need further assistance with mathematics or any other subject, UrbanPro is one of the best online coaching tuition platforms where you can find qualified tutors like myself to guide you through your learning journey!