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Measures of Central Tendency
Prove that the sum of the squares of the deviations from arithmetic mean is the least i.e. less than of the squares of the deviations of observation taken from any value.
For proving the statement given in the question we take the following observations:
1,2,3, 4,5
|
X |
X-3 |
X-4 (x') |
X'2 |
|
|
(x) |
(x2) |
|||
|
1 2 3 4 5 |
-2 -1 0 +1 +2 |
4 1 0 1 4 |
-3 -2 -1 0 +1 |
9 4 1 0 1 |
|
Σ x = 15 |
Σ x2=10 |
Σ x2= 15 |
||
We take another value i.e. 4. We observe that the sum of squares of deviations taken from mean (3) is less than that taken from other value (4) is less.
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The most suitable average for qualitative measurement is:
Which average is affect most by the presence of extreme items?
The algebraic sun of deviation of a set of n values from A.M. is =:
Comment on whether the following statements are True or False.
Following information pertains to the daily income of 150 families. Calculate the arithmetic means.
|
Income (in Rs.) |
No. of Families |
|
More than 75 More than 85 More than 95 More than 105 More than 115 More than 125 More than 135 More than 145 |
150 140 115 95 70 60 40 25 |
If the arithmetic mean of the data given below is 28, find (a) the missing frequency and (b) the median of the series.
|
Profit per retail shop (in Rs.) |
Number of retail shops |
|
0-10 10-20 20-30 30-40 40-50 50-60 |
12 18 27 – 17 6 |
The following series relates to the daily income of workers employed in a firm. Compute the (a) highest income of lowest 50% workers, (6) minimum income earned by the top 25% and (c) maximum income earned by lowest 25% workers.
|
Daily Income (in Rs.) |
Number of Workers |
|
10-14 15-19 20-24 25-29 30-34 35-39 |
5 10 15 20 10 5 |
The following table gives production yield in kg. per hectare of wheat of 150 arms in a village. Calculate the mean, median and mode production yield.
|
Production yield (kg. per hectare) |
50-53 |
53-56 |
56-59 |
59-62 |
62-65 |
65-68 |
68-71 |
71-74 |
74-77 |
|
Number of farms |
3 |
8 |
14 |
30 |
36 |
28 |
16 |
10 |
5 |
The size of land holdings of 380 families in a village is given below. Find the median size of land holdings.
|
Size of Land Holdings (in acres) |
Number of families |
|
less than 100 100-200 200-300 300-400 400 and above |
40 89 148 64 39 |
What do you mean by 'Average'?
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