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The CORRECT CHOICE is (c) 6.23

The BEST EXPLANATION: Arithmetic mean = \(\frac {Sum \, of \, the \, OBSERVATIONS}{Number \, of \, observations}\)

= \(\frac {2+8.2+3+9+11.2+4}{6}\)

= 6.23

Correct answer is (c) 4

Easy EXPLANATION: The EMPIRICAL mean median mode relation is GIVEN as

Mean – Mode = 3(Mean – Median)

Given Mean = 10 and Median = Mean – 2 = 10 – 2 = 8

10 – Mode = 3(10 – 8)

Mode = 4

The CORRECT choice is (b) \(\frac {Sum \, of \, the \, observations}{Number \, of \, observations}\)

Explanation: Arithmetic MEAN can also be called the AVERAGE of given variables in a distribution. The formula for arithmetic mean is the ratio of the sum of the observations to the number of observations.

Arithmetic mean = \(\frac {Sum \, of \, the \, observations}{Number \, of \, observations}\)

Correct option is (C) Value separating higher HALF from the lower half of a data sample

The explanation: In statistics, the MEDIAN is also called the ‘Middle Value’ as it is the value that SEPARATES the HIGHEST half from the lower half of a data sample.

The correct choice is (d) 1144

The BEST I can EXPLAIN: ARITHMETIC MEAN = \(\frac {Sum \, of \, the \, observations}{Number \, of \, observations}\)

143 = \(\frac {Sum \, of \, the \, observations}{8}\)

Sum of the observations = 143 × 8

= 1144

Right option is (a) Median = L + [(n / 2 – CF) / F] * h

Easiest explanation: Formula for the Median of Grouped Data

Median = L + [(n / 2 – c.f) / f] * h

L = Lower limit of Median CLASS

cf = Cumulative frequency of the class PRIOR to median class

f = Frequency of Median Class

h = Class size

n = Total frequency

The correct option is (a) 15

For explanation: The empirical MEAN median mode relation is given as

Mean – Mode = 3(Mean – Median)

Given Mean = 22.5 and Median = 20

22.5 – Mode = 3(22.5 – 20)

Mode = 15

Right option is (b) Statistics is the collection, classification and INTERPRETATION of data

Easiest explanation: Statistics is DERIVED from the language and is a branch of MATHEMATICS that DEALS with the collection, classification and interpretation of data.

Right answer is (c) Ronald Fisher

For EXPLANATION I would say: Sir Ronald Fisher contributed to the DEVELOPMENT of NEW theories in statistics. Statistics DEALS with the collection, classification and interpretation of data.

The correct ANSWER is (c) 10

For explanation: The empirical MEAN median MODE RELATION is given as

Mean – Mode = 3(Mean – Median)

Given Mean = 25 and Median = 20

25 – Mode = 3(25 – 20)

Mode = 10

Correct choice is (B) 5

The explanation: Mode in a data SET is defined as the number that occurs most frequently in a data set.

5 occurred three times, 7 occurred two times, 2 and 21 occurred one time each.

5 is the most repeated number ACCORDING to the definition mode.

Correct ANSWER is (c) 25

Explanation: The empirical MEAN median mode RELATION is given as

Mean – Mode = 3(Mean – Median)

25 – 25 = 3(25 – Median )

Median = 25

Right answer is (b) 33.33

To explain: The EMPIRICAL MEAN median MODE relation is given as

Mean – Mode = 3(Mean – Median)

Given Mean = 35, Mode = 30

35 – 30 = 3(35 – Median )

5 = 105 – 3 Median

Median = 33.33

Right option is (C) Both 13 and 19

For explanation I would say: In the above data SET, both 13 and 9 are repeated TWICE and a data set can have more than ONE MODE. So, the mode is both 13 and 9.

The correct option is (c) 6

Easiest EXPLANATION: ARITHMETIC mean = \(\FRAC {SUM \, of \, the \, observations}{Number \, of \, observations}\)

6.23 = \(\frac {37.4}{Number \, of \, observations}\)

Number of the observations = \(\frac {37.4}{6.23}\)

= 6

Correct option is (d) 253

For EXPLANATION I would SAY: ARITHMETIC mean = \(\FRAC {Sum \, of \, the \, observations}{Number \, of \, observations}\)

23 = \(\frac {Sum \, of \, the \, observations}{11}\)

Sum of the observations = 23 × 11

= 253

Right option is (b) 145.4

The BEST I can explain: Arithmetic MEAN = \(\frac {Sum \, of \, the \, OBSERVATIONS}{Number \, of \, observations}\)

= \(\frac {142+143+145+158+139}{5}\)

= 145.4