2 pics, one question ### Study on Attractiveness Ratings in Speed DatingIn a study of speed dating, female subjects were asked to rate the attractiveness of their male dates. The ratings were given on a scale from 1 to 10, where 1 signifies "not attractive" and 10 signifies "extremely attractive". Below is a sample of the results:#### Sample Data```7, 4, 4, 6, 8, 1, 1, 2, 4, 6, 3, 5, 69, 7, 7, 4, 7, 1, 5, 10, 8, 2, 6, 1 ```### Statistical AnalysisTo understand the distribution and variation in attractiveness ratings, we will calculate the range, variance, and standard deviation of the sample data.1. **Range**: The range of the sample data is the difference between the highest and lowest values in the data set. - **Calculation**: Range = Max Value - Min Value - Max Value = 10, Min Value = 1 - **Range** = 10 - 1 = 9 - **Rounded Range**: 9.02. **Standard Deviation**: The standard deviation measures the amount of variation or dispersion of a set of values. - **Calculation**: Use the formula for standard deviation. - Steps (Simplified): 1. Find the mean (average) of the data. 2. Subtract the mean from each data point and square the result. 3. Find the mean of these squared differences. 4. Take the square root of this mean. - **Result**: Calculated and rounded to one decimal place. - **Standard Deviation**: 2.8 (approx)3. **Variance**: The variance measures how far each number in the set is from the mean and thus from every other number in the set. - **Calculation**: Variance is the square of the standard deviation. - **Variance**: 7.8 (approx) The calculated values help us understand the spread and distribution of attractiveness ratings in this sample group, which can be generalized to describe variations among attractiveness ratings for the broader population of adult males. **Note**: Ensure the values are calculated and ### Speed Dating Study on Attractiveness RatingsIn a study of speed dating, female subjects were asked to rate the attractiveness of their male dates. The ratings were on a scale from 1 to 10, where 1 indicates "not attractive" and 10 indicates "extremely attractive." Below is a sample of the results:| 7 | 4 | 4 | 6 | 8 | 1 | 1 | 2 | 4 | 6 | 3 | 5 | 6 ||---|---|---|---|---|---|---|---|---|---|---|---|---|| 9 | 7 | 7 | 4 | 7 | 7 | 1 | 5 | 10| 8 | 2 | 6 | 1 |The goal is to find the range, variance, and standard deviation for the given sample data and determine if the results can describe the variation among attractiveness ratings for the population of adult males.#### Calculation of RangeThe range is the difference between the highest and lowest values in the dataset.- **Highest value:** 10- **Lowest value:** 1- **Range:** 10 - 1 = 9#### Calculation of VarianceVariance is a measure of how much the values in a dataset differ from the mean of the dataset.- **Mean (average) of sample data:** $ \bar{x} = \frac{\sum x_i}{n} $- Sum of sample data: $7 + 4 + 4 + 6 + 8 + 1 + 1 + 2 + 4 + 6 + 3 + 5 + 6 + 9 + 7 + 7 + 4 + 7 + 7 + 1 + 5 + 10 + 8 + 2 + 6 + 1 = 132$- Number of data points (n): 25- Mean: $ \bar{x} = \frac{132}{25} = 5.28 $To find the variance ($ \sigma^2 $):$ \sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n-1}$1. Calculate $(x_i - \bar{x})^2$ for each value.2. Sum these squared

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In a study of speed dating, female subjects were asked to rate the attractiveness of their male dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive Find the range, variance, and standard deviation for the given sample data. Can the results be used to describe the variation among attractiveness ratings for the population of adult males 4. 8 1 1 6. OI 7 7 1 10 8 6. 1 The range of the sample data is (Round to one decimal place as needed.) The standard deviation of the sample data is (Round to one decimal place as needed.) The variance of the sample data is (Round to one decimal place as needed.)

In a study of speed dating, female subjects were asked to rate the attractiveness of their male dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive Find the range, variance, and standard deviation for the given sample data. Can the results be used to describe the variation among attractiveness ratings for the population of adult males 4. 8 1 1 6. OI 7 7 1 10 8 6. 1 The range of the sample data is (Round to one decimal place as needed.) The standard deviation of the sample data is (Round to one decimal place as needed.) The variance of the sample data is (Round to one decimal place as needed.)

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Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.

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2 pics, one question

### Study on Attractiveness Ratings in Speed Dating

In a study of speed dating, female subjects were asked to rate the attractiveness of their male dates. The ratings were given on a scale from 1 to 10, where 1 signifies "not attractive" and 10 signifies "extremely attractive". Below is a sample of the results:

#### Sample Data
```
7, 4, 4, 6, 8, 1, 1, 2, 4, 6, 3, 5, 6
9, 7, 7, 4, 7, 1, 5, 10, 8, 2, 6, 1
```

### Statistical Analysis
To understand the distribution and variation in attractiveness ratings, we will calculate the range, variance, and standard deviation of the sample data.

1. **Range**: The range of the sample data is the difference between the highest and lowest values in the data set.
- **Calculation**: Range = Max Value - Min Value
- Max Value = 10, Min Value = 1
- **Range** = 10 - 1 = 9
- **Rounded Range**: 9.0

2. **Standard Deviation**: The standard deviation measures the amount of variation or dispersion of a set of values.
- **Calculation**: Use the formula for standard deviation.
- Steps (Simplified):
1. Find the mean (average) of the data.
2. Subtract the mean from each data point and square the result.
3. Find the mean of these squared differences.
4. Take the square root of this mean.
- **Result**: Calculated and rounded to one decimal place.
- **Standard Deviation**: 2.8 (approx)

3. **Variance**: The variance measures how far each number in the set is from the mean and thus from every other number in the set.
- **Calculation**: Variance is the square of the standard deviation.
- **Variance**: 7.8 (approx)

The calculated values help us understand the spread and distribution of attractiveness ratings in this sample group, which can be generalized to describe variations among attractiveness ratings for the broader population of adult males.

**Note**: Ensure the values are calculated and

### Speed Dating Study on Attractiveness Ratings

In a study of speed dating, female subjects were asked to rate the attractiveness of their male dates. The ratings were on a scale from 1 to 10, where 1 indicates "not attractive" and 10 indicates "extremely attractive." Below is a sample of the results:

| 7 | 4 | 4 | 6 | 8 | 1 | 1 | 2 | 4 | 6 | 3 | 5 | 6 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 9 | 7 | 7 | 4 | 7 | 7 | 1 | 5 | 10| 8 | 2 | 6 | 1 |

The goal is to find the range, variance, and standard deviation for the given sample data and determine if the results can describe the variation among attractiveness ratings for the population of adult males.

#### Calculation of Range
The range is the difference between the highest and lowest values in the dataset.

- **Highest value:** 10
- **Lowest value:** 1
- **Range:** 10 - 1 = 9

#### Calculation of Variance
Variance is a measure of how much the values in a dataset differ from the mean of the dataset.

- **Mean (average) of sample data:** $ \bar{x} = \frac{\sum x_i}{n} $
- Sum of sample data: $7 + 4 + 4 + 6 + 8 + 1 + 1 + 2 + 4 + 6 + 3 + 5 + 6 + 9 + 7 + 7 + 4 + 7 + 7 + 1 + 5 + 10 + 8 + 2 + 6 + 1 = 132$
- Number of data points (n): 25
- Mean: $ \bar{x} = \frac{132}{25} = 5.28 $

To find the variance ($ \sigma^2 $):

$ \sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n-1}$

1. Calculate $(x_i - \bar{x})^2$ for each value.
2. Sum these squared

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