Creating a histogram by super imposing a normal distribution  

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Creating a histogram by super imposing a normal distribution   h = histogram(data,’Normalization’,’probability’);

The correct answer and explanation is:

The correct way to create a histogram and superimpose a normal distribution on it in MATLAB is:

h = histogram(data,'Normalization','probability');  % Create histogram with probability normalization
hold on;  % Hold the current plot to superimpose the normal distribution
x = linspace(min(data), max(data), 100);  % Generate x values for the normal distribution curve
mu = mean(data);  % Calculate the mean of the data
sigma = std(data);  % Calculate the standard deviation of the data
y = normpdf(x, mu, sigma);  % Compute the normal distribution using the mean and std
plot(x, y, 'LineWidth', 2);  % Plot the normal distribution curve
hold off;  % Release the plot hold

Explanation:

  1. Histogram Creation: The histogram(data,'Normalization','probability') function is used to create a histogram of the input data, with the normalization set to 'probability'. This means that instead of plotting the raw count of occurrences in each bin, the histogram will display the probability density of the data. The area under the histogram will sum to 1, which is a standard for normalized histograms.
  2. Hold Command: hold on; is used to retain the current plot and add additional plots to it. This is necessary because you want to plot both the histogram and the normal distribution curve on the same figure.
  3. Normal Distribution Curve: To superimpose a normal distribution, we need to generate the x-values for the curve. linspace(min(data), max(data), 100) creates a range of values from the minimum to the maximum of the data to evaluate the probability density function (PDF) of a normal distribution. The normal distribution’s mean (mu) and standard deviation (sigma) are calculated using mean(data) and std(data). These values define the shape of the normal distribution.
  4. Probability Density Function (PDF): The normpdf(x, mu, sigma) function computes the normal distribution’s PDF, given the mean (mu) and standard deviation (sigma) of the data.
  5. Plotting the Curve: plot(x, y, 'LineWidth', 2) is used to plot the normal distribution curve on the same figure, with a specified line width for visibility.
  6. Releasing the Hold: hold off; releases the hold on the plot, meaning no further plotting commands will be added to the current figure unless another hold on; is used.

This process effectively visualizes how the data distribution compares to a normal distribution, making it useful for evaluating whether the data follows a normal distribution pattern.

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