Analyzing God Distribution Among 30 Families In A Village

by TextBrain Team 58 views

Hey guys! Let's dive into analyzing the distribution of gods among 30 families in a village. We've got some interesting data to unpack, and I'm excited to walk you through it. We will explore the measures of central tendency, variability, and distribution shapes to gain a comprehensive understanding of the beliefs of the village. So, let's get started and make sense of these numbers together!

Understanding the Data

So, we've got this survey about the number of gods each family in a village has. Here’s the data:

12, 8, 7, 12, 6, 1, 5, 8, 4, 10, 14, 11, 12, 12, 13, 14, 5, 2, 6, 14, 12, 8, 9, 9, 5, 7, 3, 12, 1, 2

What does this mean? Well, it tells us how many gods each of the 30 families recognizes or worships. This kind of data can give us insights into the religious practices and beliefs prevalent in the village. To properly analyze this data, we need to calculate some key statistical measures.

Measures of Central Tendency

Measures of central tendency help us find the 'average' or 'typical' value in the dataset. Let's calculate the mean, median, and mode for our data.

  • Mean (Average): The mean is the sum of all values divided by the number of values. It gives us the arithmetic average of the number of gods. To calculate this, we add up all the numbers and divide by 30.

    Mean = (12 + 8 + 7 + 12 + 6 + 1 + 5 + 8 + 4 + 10 + 14 + 11 + 12 + 12 + 13 + 14 + 5 + 2 + 6 + 14 + 12 + 8 + 9 + 9 + 5 + 7 + 3 + 12 + 1 + 2) / 30

    Mean = 237 / 30 = 7.9

    So, on average, each family in the village has about 7.9 gods.

  • Median (Middle Value): The median is the middle value when the data is arranged in ascending order. If there's an even number of data points (like in our case), the median is the average of the two middle numbers. First, we sort the data:

    1, 1, 2, 2, 3, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 11, 12, 12, 12, 12, 12, 12, 13, 14, 14, 14

    Since we have 30 data points, the middle values are the 15th and 16th numbers, which are 8 and 8.

    Median = (8 + 8) / 2 = 8

    The median number of gods is 8.

  • Mode (Most Frequent Value): The mode is the value that appears most frequently in the dataset. Looking at our sorted data, the number 12 appears the most times (6 times).

    Mode = 12

    So, the most common number of gods among the families is 12.

Measures of Variability

Measures of variability tell us how spread out the data is. We'll calculate the range and standard deviation.

  • Range: The range is the difference between the maximum and minimum values. In our data, the maximum value is 14 and the minimum value is 1.

    Range = 14 - 1 = 13

    The range is 13, indicating the spread from the lowest to the highest number of gods.

  • Standard Deviation: The standard deviation measures the dispersion of the data points around the mean. A higher standard deviation indicates greater variability. To calculate it, we use the following steps:

    1. Find the difference between each data point and the mean.
    2. Square each of these differences.
    3. Find the average of these squared differences (this is the variance).
    4. Take the square root of the variance to get the standard deviation.

    Let's calculate it:

    1. Differences from the mean:

      (12-7.9), (8-7.9), (7-7.9), (12-7.9), (6-7.9), (1-7.9), (5-7.9), (8-7.9), (4-7.9), (10-7.9), (14-7.9), (11-7.9), (12-7.9), (12-7.9), (13-7.9), (14-7.9), (5-7.9), (2-7.9), (6-7.9), (14-7.9), (12-7.9), (8-7.9), (9-7.9), (9-7.9), (5-7.9), (7-7.9), (3-7.9), (12-7.9), (1-7.9), (2-7.9)

    2. Squared differences:

      (4.1)^2, (0.1)^2, (-0.9)^2, (4.1)^2, (-1.9)^2, (-6.9)^2, (-2.9)^2, (0.1)^2, (-3.9)^2, (2.1)^2, (6.1)^2, (3.1)^2, (4.1)^2, (4.1)^2, (5.1)^2, (6.1)^2, (-2.9)^2, (-5.9)^2, (-1.9)^2, (6.1)^2, (4.1)^2, (0.1)^2, (1.1)^2, (1.1)^2, (-2.9)^2, (-0.9)^2, (-4.9)^2, (4.1)^2, (-6.9)^2, (-5.9)^2

    3. Values of Squared differences:

      16.81, 0.01, 0.81, 16.81, 3.61, 47.61, 8.41, 0.01, 15.21, 4.41, 37.21, 9.61, 16.81, 16.81, 26.01, 37.21, 8.41, 34.81, 3.61, 37.21, 16.81, 0.01, 1.21, 1.21, 8.41, 0.81, 24.01, 16.81, 47.61, 34.81

    4. Variance (Average of squared differences):

      Variance = (16.81 + 0.01 + 0.81 + 16.81 + 3.61 + 47.61 + 8.41 + 0.01 + 15.21 + 4.41 + 37.21 + 9.61 + 16.81 + 16.81 + 26.01 + 37.21 + 8.41 + 34.81 + 3.61 + 37.21 + 16.81 + 0.01 + 1.21 + 1.21 + 8.41 + 0.81 + 24.01 + 16.81 + 47.61 + 34.81) / 30

      Variance = 422.3 / 30 = 14.0767

    5. Standard Deviation (Square root of variance):

      Standard Deviation = √14.0767 ≈ 3.752

    The standard deviation is approximately 3.752, indicating a moderate spread in the number of gods among the families.

Distribution Shape

Understanding the distribution shape helps us visualize the data. Let's consider skewness.

  • Skewness: Skewness measures the asymmetry of the data distribution. If the distribution is symmetrical, the skewness is zero. If it's skewed to the right (positive skew), the tail on the right side is longer, and if it's skewed to the left (negative skew), the tail on the left side is longer. In our case:

    • Mean = 7.9
    • Median = 8

    Since the mean is slightly less than the median, the distribution is slightly skewed to the left (negatively skewed). This suggests that there are a few families with a very low number of gods, pulling the mean down.

Analyzing the Findings

So, what does all this tell us? Let's break it down:

  • Central Tendency:
    • The average (mean) number of gods is about 7.9, but the most common (mode) number is 12. The median is 8.
  • Variability:
    • The numbers vary from 1 to 14, with a standard deviation of about 3.752.
  • Distribution:
    • The distribution is slightly skewed to the left, meaning more families have a higher number of gods.

Interpretation:

The families in this village have a wide range of beliefs, with some having very few gods and others having quite a few. The fact that the mode is 12 suggests that a significant portion of families recognize or worship a larger pantheon of gods. The left skew indicates that while many families have a higher number of gods, there are some with significantly fewer, influencing the average. The moderate standard deviation implies that the distribution is fairly spread out, reflecting diverse religious practices among the families.

Conclusion

Alright, guys, that wraps up our analysis of the god distribution among the 30 families. We've seen how statistical measures can give us a clearer picture of religious diversity within the village. From the central tendencies to the variability and distribution shape, each measure adds a layer of understanding. Hope you found this insightful, and happy analyzing!