## Class 11 - Economics - Statistical Tools - Measures of Central Tendency

Q1: Define an average?

Answer: An average is a single value that represents the whole group.

Q2: Name the measures of central tendency?

Answer: Three important types of statistical averages are :
- Arithmetic Mean,
- Median and
- Mode.

Q3: What is median?

Answer: It is defined as the middle value of the series when arranged either in ascending order or in descending order.

Q4: What is mode ?

Answer: It is defined as the value which occurs most frequently in a series.

Q5: Can mode be graphically located?

Answer: Mode can be located graphically with the help of histogram.

Q6: What are the functions of average?

Average helps to get a representative value to the entire set of data.

It Facilitates Comparison.

It is a useful tool in decision- making.

Q7:  Average daily wage of 50 workers of a factory was ₹ 200. Each worker is given a raise of ₹ 20. What is the new average daily wage?

Increase is wages of each worker = ₹20.

Total increase in wages =  50 × 20 = ₹ 1000.

Total wages before increase in wages = 50 × 200= ₹ 10,000.

Total wages after increase in wages= 10,000 + 1000= ₹ 11000.

New average wages ∑X /N =  11000 / 5 =  ₹220

Thus mean wage will increase by ₹ 20.

Q8: What relationship exists between mean, median and mode in case of a symmetrical distribution?

Answer: In a symmetrical distribution, X = M = Z
Empirically, in an asymmetrical distribution, Mode = 3 median – 2 mean.

Q9: What relationship exists between X, M and Z in moderately negative skewed distribution?

Answer: In a moderately negative skewed distribution. X < M < Z .

Q10: What are the merits of arithmetic mean?

It is easy to calculate and simple to understand.
It is rigidly defined.
It is a calculated value not a positional value.
It is based on all observations.

Q11: What are the demerits of arithmetic mean?

It is affected by presence of extreme values.
It cannot be calculated in open-ended series.
It cannot be ascertained graphically.
It sometimes gives misleading and surprising results.

Q12: What are the merits of median?

It is easy to understand and easy to compute.
It is not unduly affected by extreme observations
Median can be located graphically with the help of ogives.
It is the most appropriate average in case of open-ended classes.
It is the most suitable average for qualitative measurement such as intelligence, beauty etc.
It is a positional value and not a calculated value.

Q13: What are the demerits of median?

It is not based on all observations of the series since it is a positional average.
It requires arrangement of data, but other averages do not need it.
It can not be computed exactly where the number of items in a series is even.

Q14: What are related measures of median?

Answer:  Related measures of median are:
Quartiles: Quartiles are the measures which divide the data into four equal parts, each part contains equal number of observations.

Percentiles: Percentiles divide the series into hundred equal parts. For any series, there are 99 percentiles denoted by P₁ , P₂ , P₃,..., P₉₉. P₅₀ is the median value.

Q15: What are the merits of mode?

It is easy to understand and simple to calculate.
It is not affected by the presence of extreme values.
It can be located graphically with the help of histogram.
It can be easily calculated in case of open-ended classes.

Q16: What are the demerits of mode?

It is not rigidly defined.
When frequencies of all items are identical, It is difficult to identify the Modal Value.
It is not based on all observations.
Mode is not capable of further algebraic treatment.

Q17: “Arithmetic mean is affected by very large and very small values but median and mode are not affected by them.” Explain.

Answer: Median is the value of the middle item of a series arranged in ascending or in descending order of magnitude. Mode only takes values at the points around which the items tend to be most heavily concentrated.Arithmetic mean takes into account the value of all items (i.e. very large and very small) in a series. Thus it is only the arithmetic mean which is affected by extreme values in the series.

Q18: Which average would be suitable in the following cases?
(ii) Average intelligence of students in a class.
(iii) Average Production in a factory per shift.
(iv) Average wages in an industrial concern.
(v) When the sum of absolute deviations from average is least.
(vi) In case of open-ended frequency distribution.

(i) Mode,
(ii) Median,
(iii) Mean
(iv) Mean,
(V) Median,
(vi) Median or mode.

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