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) 
Less than 100 
200300 
300200 
100200 
400 and above 
Number of families 
40 
89 
148 
64 
39 
To calculate the mean size of holding, first calculate the cumulative frequency.
Size of land holdings (in acres)(X) 
Number of families 
Cumulative frequency 
0100 
40 
40 
100200 
89 
129 
200300 
148 
277 
300400 
64 
341 
400500 
39 
380 

∑f = 380 

Following information pertains to the daily income of 150 families
Calculate the arithmetic mean.
Income (in ₹) 
Number of families 
More than 75 
150 
.. 85 
140 
.. 95 
115 
.. 105 
95 
.. 115 
70 
.. 125 
60 
.. 135 
40 
.. 145 
25 
Income (in Rs.) 
Number of families(f) 
Mid values 
fx 
7585 
10 
80 
800 
8595 
25 
90 
2250 
95105 
20 
100 
2000 
105115 
25 
110 
2750 
115125 
10 
120 
1200 
125135 
20 
130 
2600 
135145 
15 
140 
2100 
145155 
25 
150 
3750 

∑f = 150 

∑fx = 17450 
The following table gives the daily income of ten workers in a factory.
Find the arithmetic mean.
Workers 
A 
B 
C 
D 
E 
F 
G 
H 
I 
J 
Daily Income (in ₹.) 
120 
150 
180 
200 
250 
300 
220 
350 
370 
260 
Indicate the most appropriate alternative from the multiple choices provided against each question.
i. The most suitable average for qualitative measurement is
ii. Which average is affected most by the presence of extreme items?
iii. The algebraic sum of deviation of a set of n values from A.M is
The following table gives production yield in kg. per hectare of wheat of 150 farms in a village. Calculate the mean, median and mode values.
Production yield (kg. per hectare) 
5053 
5356 
5659 
5962 
6265 
6568 
6871 
7174 
7477 
Number of farms 
3 
8 
14 
30 
36 
28 
16 
10 
5 
To calculate mean, median and mode values
Production yield (kg per hectare) (X) 
Number of farms 
Mid values (m) 
Cumulative Frequency (cf) 
fm 
5053 
3 
51.5 
3 
154.5 
5356 
8 
54.5 
11 
436 
5659 
14 
57.5 
25 
805 
5962 
30 
60.5 
55 
1815 
6265 
36 
63.5 
91 
2286 
6568 
28 
66.5 
119 
1862 
6871 
16 
69.5 
135 
1112 
7174 
10 
72.5 
145 
725 
7477 
5 
75.5 
150 
377.5 

∑f = 150 


∑fm = 9573 
The following series relates to the daily income of workers employed in affirm. Compute (a) highest income of lowest 50% workers (b) minimum income earned by the top 25% workers and (c) maximum income earned by 25% workers.
Daily Income (in ₹) 
1014 
1519 
2024 
2529 
3034 
3539 
Numbers of workers 
5 
10 
15 
20 
10 
5 
Daily income(in ₹) 
Class interval 
Number of workers (f) 
Cumulative frequency (cf) 
1014 
9.514.5 
5 
5 
1519 
14.519.5 
10 
15 
2024 
19.524.5 
15 
30 
2529 
24.529.5 
20 
50 
3034 
29.534.5 
10 
60 
3539 
34.539.5 
5 
65 


∑f = 65 

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 ₹) 
010 
10 20 
2030 
3040 
4050 
5060 
Number of retail shops 
12 
18 
27 
 
17 
6 
1. Let us take the missing frequency as x
Profit per retail shop (in ₹) (X) 
Number of retail shops (f) 
Mid values (m) 
fm 
010 
12 
5 
60 
1020 
18 
15 
270 
2030 
27 
25 
675 
3040 
X 
35 
35x 
4050 
17 
45 
765 
5060 
6 
55 
330 

∑f = 80 + x 

∑Fm = 2100 + 35x 
Mean = ∑fm/∑f Mean = 28
Substituting the values in the formula we get,
Thus, the missing value frequency is 20.
(b)
Profit per retail shop(in ₹) (X) 
Number of retail shops (f) 
Cumulative frequency (cf) 
010 
12 
12 
1020 
18 
30 
2030 
27 
57 
3040 
20 
77 
4050 
17 
94 
5060 
6 
100 

∑f = 100 

Comment whether the following statements are true or false.
i. The sum of deviation of items from median is zero.
False
Explanation: Generally, sum of deviations from mean is zero; but only in the case of symmetric distribution (mean=median=mode) above statement is true.
ii. An average alone is not enough to compare series.
True
Explanation: Averages are very rigid values, they don’t say anything about the variability of the series, and thus they are not enough to compare series.
iii. Arithmetic mean is a positional value.
False
Explanation: Arithmetic mean is not a positional value because it is calculated on the basis of all the observations.
iv. Upper quartile is the lowest value of top 25% of items.
True
Explanation: Quartile refers to a quarter, so when the frequency is arranged in a ascending order the upper quartile refers to the first 25% of the items.
v. Median is unduly affected by extreme observations.
False
Explanation: Median doesn’t get affected by extreme observations because it only takes the median class to calculate it. It is mean which gets affected by extreme observations.
Which average would be suitable in following cases?
i. Average size of readymade garments.
Mode
Explanation: Mode is suitable average for average size of readymade garments because it gives the most frequent occurring value.
ii. Average intelligence of students in a class.
Median
Explanation: Median is a suitable average in case of a qualitative nature of the data.
iii. Average production in a factory per shift.
Mean
Explanation: Production can be measured on a quantitative scale so Arithmetic mean is suitable in this case.
iv. Average wage in an industrial concern.
Mean
Explanation: Wage can be measured on a quantitative scale so arithmetic mean is suitable in this case.
v. When the sum of absolute deviations from average is least.
Mean
Explanation: Mean shall be used because sum of deviations from mean is always zero or least than the other averages.
vi. When quantities of the variable are in ratios.
Mean
Explanation: Ratios are quantitative, so it is suitable to use arithmetic mean.
vii. In case of openended frequency distribution.
Median
Explanation: Median is used because there is no need to adjust class size or magnitude for using median.
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