If all the values in a data set are converted to z-scores, the shape of the distribution of the z-scores will not be the same as the distribution of the original data. True or False?
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True. When all the values in a data set are converted to z-scores, the shape of the distribution of the z-scores will not be the same as the distribution of the original data. The distribution of the original data may have outliers, skewness, or kurtosis, while the distribution of the z-scores will always have a mean of 0 and a standard deviation of 1.
True. When converting a data set to z-scores, also known as standardizing the data, the shape of the distribution of the z-scores will be the same as the distribution of the original data.
To convert a data set to z-scores, you need to follow these steps:
1. Calculate the mean (μ) and standard deviation (σ) of the original data set.
2. For each value in the data set, subtract the mean (μ) from the value and then divide the result by the standard deviation (σ).
3. The resulting values are the z-scores for each data point.
By converting the data to z-scores, you are essentially transforming the data so that it has a mean of 0 and a standard deviation of 1. This allows you to compare and analyze the data in a standardized manner.
Importantly, the distribution of the z-scores will have the same shape (e.g., normal distribution, skewed, etc.) as the distribution of the original data. The z-scores simply provide a way to express the data in terms of standard deviations away from the mean, facilitating comparisons and analysis.