Answer to Question #189709 in Statistics and Probability for prince

Question

The diameters of the spores of lycopodium can be found by an interference method. The results of such an experiment are given below. The constant factor k = 5880 when the diameters are measured in cm

the following is the table

k x diameter (cm) :14 15 16 17 18 19 20 21 22 23

Number of spores :1 1 8 24 48 58 35 16 8 1

(a) Find the mean diameter of the spores.

(b) Calculate the standard deviation from the mean.

(c) Draw a normalised histogram of the data. (d) Plot the corresponding normal frequency curve on the same set of axes. 

Answer 1

Mean Diameter of spores is determined as: $\frac{Sum\:of\:total\:diameter\:of\:each\:spore}{Total\:Number\:of\:spores}=\frac{185}{10\:}=18.5$

Standard Deviation of mean is calculated as: $SD=\sqrt{\frac{\sum _{i=1}^n\:\left(X_i-\overline{X}\right)^2}{n-1}}$

$SD=\sqrt{\frac{\sum _1^{10}\:\left(185-18.5\right)^2}{10-1}}\:=55.5$