With the help of following data, prove that the sum of the deviations of items about arithmetic mean is always equal to zero.
X : 4, 6, 8, 10 and 12.
|
X |
D (X- |
|
4 6 8 10 12 |
-4 -2 0 +2 +4 |
|
Σ X = 40 |
Σ D = 0 |
From the given data it has been proved that the sum of the deviations of items about the arithmetic mean is equal to zero. Symbolically
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'?
Pocket expenditures of 6 students are (Rs.) 6,12,18,24,30 and 36 respectively. Find out arithmetic mean.
Name various kinds of statistical averages?
Mock Test Series
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