Worksheet Solutions: Measures of Central Tendency | Economics Class 11 - Commerce PDF Download

Multiple Choice Questions

Q1: Which of the following is/are objectives of averages?
(i) To facilitate comparison.
(ii) To help in decision-making.
(iii) To trace mathematical relation.
(iv) To understand the features of the problem.
Choose from the options below.
(a) (i), (ii), (iii)
(b) (ii), (iii), (iv)
(c) (i), (iii), (iv)
(d) All of these
Ans: d

Q2: The average daily wage of a group of 100 workers was ₹ 250. Each worker is now given a raise of ₹ 50. What is the new average daily wage?
(a) 200
(b) 250
(c) 300
(d) 350
Answer: c

Q3: Arithmetic mean of a group of 50 students in an exam is 48. If marks of every student are reduced by 3, the new average will be
(a) 45
(b) 48
(c) 51
(d) Can’t be calculated
Ans: a

Q4: The most used method of central tendency is median. Choose from the options below.
(a) True
(b) False
(c) Partially true
(d) Incomplete statement
Ans: b

Q5: Broadly, arithmetic mean is of ……… types.
(a) two
(b) three
(c) four
(d) five
Answer: a

Q6: Choose the incorrect statement from given below.
(a) A good average is the one which is least affected by sampling fluctuations
(b) An average should be rigidly defined
(c) An average is based on the extreme observations of the statistical distribution
(d) An average should be capable of further algebraic treatment
Ans: c

Q7: When arithmetic mean is calculated using assumed mean and the sum of deviation from assumed mean is zero, which of the below statement is correct in that situation?
(a) Assumed mean is equal to actual mean
(b) Assumed mean is less than actual mean
(c) Assumed mean is more than actual mean
(d) It’s an exception
Ans: a

Q8: A distribution of three components with total number of terms being 200, 250 and 300 with means 25, 10 and 15 respectively. The combined mean will be equal to
(a) 200
(b) 240
(c) 300
(b) Can’t be determined
Ans: b

Q9: Which of the following values of quartiles is equal to median?
(a) Q1
(b) Q2
(c) Q3
(d) None of these
Ans: b

Q10: The sum of square of deviations from actual mean is
(a) minimum
(b) maximum
(c) zero
(d) not defined
Ans: a

Q11: Arithmetic mean can be calculated under which of the following series?
(a) Cumulative series
(b) Open ended series
(c) Unequal frequency distribution
(d) All of the above
Ans: d

Q12: Choose the correct option when equal weights are assigned to all the observations of the data.
(a) Weighted mean > Arithmetic mean
(b) Weighted mean < Arithmetic mean
(c) Weighted mean = Arithmetic mean
(d) They are not related
Ans: c

Q13: Combined mean method can be used to combine arithmetic mean of ……… series.
(a) 2
(b) 3
(c) 5
(d) N-number
Ans: d

Q14: Median of a given series is ‘k’. If all the item values of series are increased by ‘k’, then what will be the new median?
(a) 2k
(b) k2
(c) k +2
(d) Can’t be determined
Ans: d

Q15: Calculation of mean in which of the following series is not accurate?
(a) Exclusive continuous series
(b) Inclusive continuous series
(c) Open-ended series
(d) Unequal class interval series
Ans: c

Q16: Mode can be calculated only if the series is ……… .
(a) inclusive
(b) exclusive
(c) Both (a) and (b)
(d) Neither (a) nor (b)
Ans: b

Q17: A frequency distribution with more than 2 modal values, is known as
(a) Bi-modal frequency distribution
(b) Tri-modal frequency distribution
(c) Multi-modal frequency distribution
(d) None of the above
Ans: c

Q18: The lowest value of highest 25 percent items of the series is known as lower quartile. Choose from the options below.
(a) True
(b) False
(c) Partially true
(d) Incomplete statement
Ans: b

Q19: What will be the median of the following series? 2, 5, 3, 4, 8, 10, 12
(a) 4
(b) 5
(c) 8
(d) 10
Ans: b

Q20: Refer to the data given in question no. 55, what will be the value of Q3?
(a) 10
(b) 10.50
(c) 0.75
(d) 11
Ans: c

Q21: Choose the correct statement about median.
(a) Highest value of lowest 25%of the items
(b) Lowest value of highest 25%of the items
(c) Highest value of lowest 50%of the items
(d) All of the above statements are false
Ans: c

Q22: Refer to the data given in question no. 55, what will be the value of Q1?
(a) 0.25
(b) 4.25
(c) 5.75
(d) 8.25
Ans: a

Q23: The mean of a given items 5, 6, 7, X, 11 and 13 is 44. Value of X will be
(a) 200
(b) 222
(c) 224
(d) 254
Ans: b

Q24: Choose the incorrect statement.
(a) Mode cannot be calculated in open-ended distributions
(b) Median is affected by change in extreme values
(c) Median is not affected by fluctuations in sampling
(d) All of the above is incorrect
Ans: d

Short Answer Questions

Q1: Define an average.
Ans: A single value that represents the typical or central value in a set of data.

Q2: What is meant by 'Central Tendency'?
Ans: Central tendency refers to the measure that represents the center or middle of a data set, indicating a typical or central value.

Q3: State two functions of an average.
Ans: Summarizing data.
Making comparisons between different data sets.

Q4: Name three measures of central tendency.
Ans: Mean, Median, Mode.

Q5: Give the formula for Weighted Arithmetic Mean.
Ans: Weighted Arithmetic Mean = Σ(xi * wi) / Σwi, where xi is the data value, and wi is the weight assigned to each value.

Q6: What is Arithmetic Mean?
Ans: Arithmetic Mean is the sum of all values in a data set divided by the number of values, representing the average.

Q7: Name two types of arithmetic mean.
Ans: Simple Arithmetic Mean and Weighted Arithmetic Mean.

Q8: What is median?
Ans: Median is the middle value in a data set when values are arranged in ascending or descending order, or the average of the two middle values in the case of an even number of values.

Q9: What are quartiles?
Ans: Quartiles are values that divide a data set into four equal parts, representing the 25th, 50th (median), and 75th percentiles.

Q10: What are percentiles?
Ans: Percentiles are values that divide a data set into 100 equal parts, indicating the relative position of a data point within the data distribution.

Q11: What are partition values?
Ans: Partition values are values that divide a data set into specified segments or partitions, such as quartiles or percentiles.

Q12: What is mode?
Ans: Mode is the value that appears most frequently in a data set.

Q13: Give the formula for finding the median in the case of a continuous series.
Ans: Median = L + [(N/2 - F) / f] * C, where L is the lower boundary of the median group, N is the total number of data points, F is the cumulative frequency before the median group, f is the frequency of the median group, and C is the class width.

Q14: Give the formula for finding the mode of a continuous series.
Ans: Mode = L + [(f1 - f0) / (2f1 - f0 - f2)] * C, where L is the lower boundary of the modal class, f0 is the frequency before the modal class, f1 is the frequency of the modal class, f2 is the frequency after the modal class, and C is the class width.