1. Descriptive statistics are widely used in qualitative research. When establishing if a population is normally distributed explain when the statistics of sample size, mean, mode, median, skewness and kurtosis will guide the researcher to make conclusions of a normal distribution
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When trying to determine if a population is normally distributed, several statistics can guide a researcher to make conclusions. Let's go over these statistics and how they can be helpful:
1. Sample Size: The larger the sample size, the more reliable the conclusions about the population distribution. As the sample size increases, the distribution of the data tends to approximate a normal distribution, following the Central Limit Theorem. So, a larger sample size increases confidence in assuming normality.
2. Mean: The mean is the arithmetic average of a set of data. In a normal distribution, the mean, mode, and median are all equal. So, if the sample mean is close to the mode and median, this suggests a normal distribution. However, it's important to remember that the mean alone cannot determine normality.
3. Mode: The mode is the value that occurs most frequently in a set of data. In a normal distribution, there is only one mode. If the sample mode is similar to the mean and median, it provides evidence for a normal distribution.
4. Median: The median is the middle value in a sorted set of data. In a perfectly normal distribution, the median should be the same as the mean and mode. If the sample median is approximately equal to the mean and mode, this supports the assumption of normality.
5. Skewness: Skewness measures the asymmetry of a distribution. In a perfectly symmetrical normal distribution, the skewness should be zero. Positive skewness indicates a longer right tail, while negative skewness indicates a longer left tail. Extreme values of skewness may suggest a departure from normality.
6. Kurtosis: Kurtosis measures the heaviness of the tails of a distribution. In a normal distribution, the kurtosis is typically around 3. If the kurtosis value is significantly higher or lower than 3, it suggests that the distribution has heavier or lighter tails, respectively.
To sum up, it is not just one statistic that determines normality, but rather a combination of factors. Researchers should consider the sample size, inspect the mean, mode, median, skewness, and kurtosis of the data to make an informed conclusion about the normality of a population distribution. It is also helpful to use graphical tools like histograms or Q-Q plots to visualize the data distribution.