Chapter 5: Measures of Central Tendency
EXERCISES
1. Which average would be suitable in the following cases?
(i) Average size of readymade garments.
(ii) Average intelligence of students in a class.
(iii) Average production in a factory per shift.
(iv) Average wage in an industrial concern.
(v) When the sum of absolute deviations from average is least.
(vi) When quantities of the variable are in ratios.
(vii)In case of open-ended frequency distribution.
Ans-
2. Indicate the most appropriate alternative from the multiple choices provided against each question.
(i) The most suitable average for qualitative measurement is
(a) arithmetic mean
(b) median
(c) mode
(d) geometric mean
(e) none of the above
Ans-
(ii) Which average is affected most by the presence of extreme items?
(a) median
(b) mode
(c) arithmetic mean
(d) none of the above
Ans-
(iii) The algebraic sum of deviation of a set of n values from A.M. is
(a) n
(b) 0
(c) 1
(d) none of the above
[Ans. (i) b (ii) c (iii) b]
3. Comment whether the following statements are true or false.
(i) The sum of deviation of items from median is zero.
(ii) An average alone is not enough to compare series.
(iii) Arithmetic mean is a positional value.
(iv) Upper quartile is the lowest value of top 25% of items.
(v) Median is unduly affected by extreme observations.
[Ans. (i) False (ii) True (iii) False (iv) True (v) False]
4. 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) 0-10 10-20 20-30 30-40 40-50 50-60
Number of retail shops 12 18 27 - 17 6
(Ans. The value of missing frequency is 20 and value of the median is
Rs 27.41)
5. 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 Rs) 120 150 180 200 250 300 220 350 370 260
(Ans. Rs 240)
6. Following information pertains to the daily income of 150 families.
Calculate the arithmetic mean.
Income (in Rs) Number of families
More than 75 150
,, 85 140
,, 95 115
,, 105 95
,, 115 70
,, 125 60
,, 135 40
,, 145 25
(Ans. Rs 116.3)
7. 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 100 100–200 200 – 300 300–400 400 and above.
Number of families
40 89 148 64 39
(Ans. 241.22 acres)
8. The following series relates to the daily income of workers employed in
a firm. Compute (a) highest income of lowest 50% workers (b) minimum
income earned by the top 25% workers and (c) maximum income earned
by lowest 25% workers.
Ans-
