Question

The primary data on the income (Ls) of the company employees are given:
140, 150, 150, 200, 200, 250, 250, 250, 300, 200, 250, 400, 400, 400, 400, 500, 450, 400, 350, 100, 120, 130, 140, 110, 120,
700, 800, 700, 400, 500
Form a variation series (simple and frequency). Calculate the mean, variance. Find mode and median.
Convert variation series to interval. The calculation of the width of the interval is performed according
to the Sturges formula. Find mode and median.

Answer 1

X	(X - X̄)²
140	16.00
150	12.00
150	6.00
200	8.00
200	10.00
250	12.00
250	8.000
250	14.000
300	10.000
200	8.000
250	4268.444
400	7168.444
400	7168.444
400	7168.444
400	7168.444
500	34101.778
450	18135.111
400	7168.444
350	1201.778
100	46368.444
120	38155.111
130	34348.444
140	30741.778
110	42161.778
120	38155.111
700	147968.4444
800	234901.7778
700	147968.4444
400	7168.4444
500	34101.7778

	X	(X - X̄)²
total sum	9460	895692.89
n	30	30

mean =    ΣX/n =    9460.000   /   30   =   315.3333
                      
sample variance =    Σ(X - X̄)²/(n-1)=   895692.8889   /   29   =   30885.962
                      
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   (895692.8889/29)   =       175.7440

mode= highest frequency data =    400

Median=0.5(n+1)th value =    15.5th   value of sorted data
=   250.000  

Category / Class	Lower	Upper	Frequency	Relative Frequency
100 - 200	100	200	9	30%
200 - 300	200	300	7	23%
300 - 400	300	400	2	7%
400 - 500	400	500	7	23%
500 - 600	500	600	2	7%
600 - 700	600	700	0	0%
700 - 800	700	800	2	7%
800 - 900	800	900	1	3%

THANKS

revert back for doubt

please upvote