Question 1: (Marks: 5+10=15)

a) Compute the mean deviation from the following data.

Groups	30-34	35-39	40-44	45-49	50-54
Frequency	10	15	5	11	9

Sol:

Necessary calculation for “mean deviation”.

Groups	Frequency ()			i.e.
30-34	10	32	320	-9.4	9.4	94
35-39	15	37	555	-4.4	4.4	66
40-44	5	42	210	0.6	0.6	3
45-49	11	47	517	5.6	5.6	61.6
50-54	9	52	468	10.6	10.6	95.4
Total	50		2070			320

Mean (Arithmetic mean) is

So mean deviation is

= Ans.

b) The mean of 5 observations is 15 and variance is 9. If two more observations having values -3 and 10 are combined with these 5 observations, what will be the new mean and variance of 7 observations?

Sol:

Now sum of seven observations is i.e.

So the mean of seven observations is

Now variance of seven observations is so

Now

Ans.

Question 2: (Marks: 5+10=15)

a) Mean and the standard deviation of a set of values is 100 and 5. Compute mean ±2S.D and mean ±3S.D. Also interpret the results in the light of (i) empirical rule (ii) Chebychev’s inequality.

Sol: given

So calculations of intervals are

(i) Empirical rule

For interval (90,110)

Approximately 95% of the measurements will fall within standard deviations of the mean.

For interval (85,115)

Approximately 100% of measurements will fall within standard deviations of the mean.

(ii) Chebychev’s inequality

For interval (90,110)

At least of the observations will fall within standard deviations of the mean,

For interval (85,115)

At least of the observations will fall within standard deviations of the mean.

b) Find the first four moments about X= 174.5 as well as about mean for the following frequency distribution.

Weights (pounds)	Frequency
110-119	1
120-129	4
130-139	17
140-149	28
150-159	25
160-169	18
170-179	13
180-189	6
190-199	5
200-209	2
210-219	1
Total	…

-End-

Sol:

Weight
110-119	114.5	1	-60	-60	3600	-216000	12960000
120-129	124.5	4	-50	-200	10000	-500000	25000000
130-139	134.5	17	-40	-680	27200	-1088000	43520000
140-149	144.5	28	-30	-840	25200	-756000	22680000
150-159	154.5	25	-20	-500	10000	-200000	4000000
160-169	164.5	18	-10	-180	1800	-18000	180000
170-179	174.5	13	0	0	0	0	0
180-189	184.5	6	10	60	600	6000	60000
190-199	194.5	5	20	100	2000	40000	800000
200-209	204.5	2	30	60	1800	54000	1620000
210-219	214.5	1	40	40	1600	64000	2560000
Total				-2200	83800	-2614000	113380000
total/n					698.33	-21783.33	944833.33

If want the full file call