Mean, Median, And Mode Of Variables Age And Monthly Income ✓ Solved

Mean Median Modethe Variables Age And Monthly Income Were Chosen For T

The analysis focuses on two key quantitative variables: Age and Monthly Income. Both variables are measured on a ratio scale, making measures of central tendency such as mean, median, and mode, as well as measures of dispersion like standard deviation and variance, appropriate for describing their distributions.

The descriptive statistics for these variables reveal key insights into the sample population. For Age, the mean is 31.35 years, indicating that the average participant is approximately 31 years old. The median age is 28 years, suggesting that half of the participants are aged 28 or younger. The mode for Age is 25 years, which is the most frequently occurring age among participants. The variance for Age is 136.7112, and the standard deviation is 11.6924 years, implying a moderate spread around the mean, with most ages falling within roughly 12 years of the average.

For Monthly Income, the mean income is $2599.37, indicating that, on average, participants earn approximately $2600 per month. The median income is $1828, meaning 50% of participants have an income below this value. The mode of Monthly Income is $1296, which is the most common income level in the sample. The variance is reported as 0.6128, with a standard deviation of approximately $1681.09, revealing a high degree of variability and income disparity among the participants.

In the context of probabilities, the analysis provides estimates for the likelihood that participants' monthly incomes fall within certain ranges. The probability that a participant's income is between $1 and $1500 is 0.4135, indicating about 41.35% chance of income within this bracket. The probability extends to higher income ranges: the probability for incomes between $1501 and $3000 is 0.2692, for $3001 to $4500 is 0.1538, and for incomes of $4501 or more is 0.1635. These probabilities collectively offer insight into the income distribution's skewness and spread, showing that a substantial proportion of participants earn less than $1500, while others are spread across higher income brackets.

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The analysis of demographic and economic variables such as Age and Monthly Income provides significant insights into the characteristics and socioeconomic status of the sampled population. Descriptive statistics are fundamental in summarizing and understanding data distributions, and measures such as mean, median, mode, variance, and standard deviation serve to provide a comprehensive overview.

The mean age of 31.35 years suggests that the population skews towards young adults, potentially indicating a relatively youthful workforce or demographic segment. The median age of 28 years further emphasizes this, as it indicates that half of the participants are at or below this age, reflecting a concentration among younger individuals. The mode being 25 years suggests that this is the most common age, perhaps indicating a typical entry-level or early-career demographic. The variance and standard deviation statistics reveal that while the ages are centered around the mean, there is a considerable spread—about 11.7 years—highlighting the diversity in age within the sample.

For Monthly Income, the average earning of approximately $2600 suggests a mid-level income bracket within the context of the population studied. The median income of $1828 indicates that half of the participants earn less than this, highlighting income inequality or variance in earning levels. The mode at $1296 represents the most frequently reported income, possibly reflecting a common income level or rate within the sample group. The high variance and standard deviation, in particular, suggest a wide disparity in income levels among participants, with some earning significantly more or less than the average.

The probability analysis of income ranges provides further insights into income distribution. The probability that a participant's income falls between $1 and $1500 is approximately 41.35%, illustrating that a substantial portion of the sample earns low to moderate incomes. Probabilities for higher income categories decrease progressively, but a notable 16.35% earn $4501 or more, indicating a dual income distribution with both lower and higher earners present. These findings are crucial in understanding socioeconomic stratification within the population, with implications for targeted policy interventions or resource allocations.

In conclusion, the combined analysis of central tendency measures, dispersion, and probability distributions underscores the diverse nature of the sample population in terms of age and income. Such statistical characterizations are essential in social science research, informing policymakers and stakeholders about the population's demographic and economic profile. Recognizing the variability and distribution patterns enables more nuanced decision-making and targeted strategies to address potential disparities.

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