Tabulated Data

Here are the first 20 out of 200 random numbers generated:

Index	Random Numbers
0	0.496714
1	-0.138264
2	0.647689
3	1.523030
4	-0.234153
5	-0.234137
6	1.579213
7	0.767435
8	-0.469474
9	0.542560
10	-0.463418
11	-0.465730
12	0.241962
13	-1.913280
14	-1.724918
15	-0.562288
16	-1.012831
17	0.314247
18	-0.908024
19	-1.412304

Descriptive Statistics

The descriptive statistics for these 200 random numbers are as follows:

Statistic	Value
Count	200.000000
Mean	-0.040771
Std Dev	0.931004
Min	-2.619745
25%	-0.705128
50% (Median)	-0.004192
75%	0.500852
Max	2.720169

Graphical Representation

The distribution of the 200 random numbers is shown in the histogram above. It includes a Kernel Density Estimate (KDE) overlay, which provides a smooth curve representing the distribution.

Interpretation:

1. Mean and Median: The mean is slightly negative at $-0.040771$, and the median is nearly zero, indicating that the data is approximately centered around zero, as expected for a standard normal distribution.

2. Standard Deviation: The standard deviation is close to 1 ($0.931004$), consistent with the standard normal distribution's properties.

3. Range: The minimum value is $-2.619745$ and the maximum is $2.720169$, indicating that the data points are within a typical range for a standard normal distribution (about $-3$ to $3$).

4. Distribution Shape: The histogram shows that the data follows a bell-shaped curve, characteristic of a normal distribution. The KDE plot aligns well with the histogram, further confirming the normality of the data.

Would you like to explore any specific aspects of this analysis further, or do you have any additional questions?

Related Questions:

1. How would the distribution change if the random numbers were generated from a uniform distribution?
2. What would the descriptive statistics look like for a skewed distribution?
3. How can you test if this data follows a normal distribution?
4. What is the significance of the 25th and 75th percentiles in this context?
5. How would outliers affect the mean and standard deviation?

Tip: When analyzing data, always check the distribution shape along with summary statistics to get a complete understanding of the dataset.