In: Math
The numbers 1,6,15,20,15,6,1 are the coefficients of the binominal expansion (p+q)^6. Use the normal quantile plot method to show that these numbers are close to a normal distribution.
first sort the values in ascending order
1 |
1 |
6 |
6 |
15 |
15 |
20 |
here we have 7 values so divide the standard normal distribution into 8 equal-sized areas with 7 values. so each segment has 12.5% area
find z values for each of the segment
probability | z values | |
12.5 | 0.125 | -1.15035 |
25 | 0.25 | -0.67449 |
37.5 | 0.375 | -0.31864 |
50 | 0.5 | -1.4E-16 |
62.5 | 0.625 | 0.318639 |
75 | 0.75 | 0.67449 |
87.5 | 0.875 | 1.150349 |
i have used excel to find out z scores(NORMSINV)
now plot the graph with the following values
actual quantiles | theoretical quantiles |
1 | -1.15034938 |
1 | -0.67448975 |
6 | -0.318639364 |
6 | -1.39214E-16 |
15 | 0.318639364 |
15 | 0.67448975 |
20 | 1.15034938 |
here R-value is 0.916. straight line is good fit for data
straight line on q q plot indicates the data is approximately normal.
The numbers 1,6,15,20,15,6,1 are close to a normal distribution.
remark:i have used excel to draw the graph