The distributions can have any shape that you like.
the midpoint of the data set
The assumption that works best for a large data set with a normal distribution is that the data follows a bell-shaped curve, characterized by symmetry around the mean. In this context, the Central Limit Theorem supports that as the sample size increases, the sampling distribution of the sample mean will also approach a normal distribution, regardless of the original data's distribution. This allows for the application of parametric statistical methods, such as t-tests or ANOVA, which rely on normality. Additionally, it is assumed that the data points are independent of each other.
A bimodal distribution.
To compute frequency count, first, collect your data set, which can be a list of items or observations. Then, categorize the data by identifying unique items or values and tally how many times each appears in the data set. Finally, record these tallies to create a frequency table, where each unique item is listed alongside its corresponding count. This process helps in analyzing the distribution of data points within the set.
A box and whisker plot does not provide specific values for individual data points, nor does it indicate the frequency of those data points. While it summarizes the distribution of the data through quartiles, it does not reveal the shape of the distribution or any potential outliers beyond the whiskers. Additionally, it does not show the mean or median unless explicitly marked.
You describe the shape, not of the data set, but of its density function.You describe the shape, not of the data set, but of its density function.You describe the shape, not of the data set, but of its density function.You describe the shape, not of the data set, but of its density function.
A normal data set is a set of observations from a Gaussian distribution, which is also called the Normal distribution.
the midpoint of the data set
The answer will depend on the set of data!
Frequently it's impossible or impractical to test the entire universe of data to determine probabilities. So we test a small sub-set of the universal database and we call that the sample. Then using that sub-set of data we calculate its distribution, which is called the sample distribution. Normally we find the sample distribution has a bell shape, which we actually call the "normal distribution." When the data reflect the normal distribution of a sample, we call it the Student's t distribution to distinguish it from the normal distribution of a universe of data. The Student's t distribution is useful because with it and the small number of data we test, we can infer the probability distribution of the entire universal data set with some degree of confidence.
Frequently it's impossible or impractical to test the entire universe of data to determine probabilities. So we test a small sub-set of the universal database and we call that the sample. Then using that sub-set of data we calculate its distribution, which is called the sample distribution. Normally we find the sample distribution has a bell shape, which we actually call the "normal distribution." When the data reflect the normal distribution of a sample, we call it the Student's t distribution to distinguish it from the normal distribution of a universe of data. The Student's t distribution is useful because with it and the small number of data we test, we can infer the probability distribution of the entire universal data set with some degree of confidence.
anonymously
xz
The normal distribution allows you to measure the distribution of a set of data points. It helps to determine the average (mean) of the data and how spread out the data is (standard deviation). By using the normal distribution, you can make predictions about the likelihood of certain values occurring within the data set.
The assumption that works best for a large data set with a normal distribution is that the data follows a bell-shaped curve, characterized by symmetry around the mean. In this context, the Central Limit Theorem supports that as the sample size increases, the sampling distribution of the sample mean will also approach a normal distribution, regardless of the original data's distribution. This allows for the application of parametric statistical methods, such as t-tests or ANOVA, which rely on normality. Additionally, it is assumed that the data points are independent of each other.
range
A bimodal distribution.