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: $SD=\sqrt{\frac{\sum _{i=1}^n\:\left(X_i-\overline{X}\right)^2}{n-1}}$

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