Mathematics Questions and Answers – Statistics – Mean of Grouped Data

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Statistics – Mean of Grouped Data”.

1. What is statistics?
a) Statistics is the collection of data
b) Statistics is the collection, classification and interpretation of data
c) Statistics is the classification of data
d) Statistics is the interpretation of data

Explanation: Statistics is derived from the language and is a branch of mathematics that deals with the collection, classification and interpretation of data.

2. Who is the pioneer that contributed to the development of statistics?
a) Albert Einstein
b) Lewis Capaldi
c) Ronald Fisher
d) Harold Fisher

Explanation: Sir Ronald Fisher contributed to the development of new theories in statistics. Statistics deals with the collection, classification and interpretation of data.

3. What is Range?
a) Largest value – Smallest value
b) Smallest value – Largest value
c) Mid value – Average value
d) Average value – Mid value

Explanation: Range is defined as the difference between the largest value and the smallest value of the variable in a distribution.
R = L – S     where L = Largest value, S = Smallest value.
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4. What is the formula for the arithmetic mean?
a) $$\frac {Number \, of \, the \, observations}{Sum \, of \, observations}$$
b) $$\frac {Sum \, of \, the \, observations}{Number \, of \, observations}$$
c) $$\frac {Product \, of \, the \, observations}{Number \, of \, observations}$$
d) $$\frac {Sum \, of \, the \, observations}{Product \, of \, the \, observations}$$

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 = $$\frac {Sum \, of \, the \, observations}{Number \, of \, observations}$$

5. Mean of the data can be represented as x = $$\frac {\sum f i xi}{\sum fi}$$.
a) False
b) True

Explanation: Let f1, f2 …. fn are the frequencies of respective observations x1, x2 …. xn. Then the mean of the data can be written as x = $$\frac {f1 x1+f2x2+⋯+fnxn}{f1+f2+⋯+fn}$$
x = $$\frac {\sum f i xi}{\sum fi}$$

6. What is the arithmetic mean of the observations 2, 8.2, 3, 9, 11.2, 4?
a) 5.5
b) 8.45
c) 6.23
d) 7.1

Explanation: Arithmetic mean = $$\frac {Sum \, of \, the \, observations}{Number \, of \, observations}$$
= $$\frac {2+8.2+3+9+11.2+4}{6}$$
= 6.23

7. What is the mean of 142, 143, 145, 158, 139?
a) 135.4
b) 145.4
c) 0.23
d) 135.5

Explanation: Arithmetic mean = $$\frac {Sum \, of \, the \, observations}{Number \, of \, observations}$$
= $$\frac {142+143+145+158+139}{5}$$
= 145.4

8. Find the sum of the observations if the mean is 143 and the number of observations is 8.
a) 1148
b) 1344
c) 1244
d) 1144

Explanation: Arithmetic mean = $$\frac {Sum \, of \, the \, observations}{Number \, of \, observations}$$
143 = $$\frac {Sum \, of \, the \, observations}{8}$$
Sum of the observations = 143 × 8
= 1144

9. Find the sum of the observations if the mean is 23 and the number of the observations is 11?
a) 283
b) 256
c) 293
d) 253

Explanation: Arithmetic mean = $$\frac {Sum \, of \, the \, observations}{Number \, of \, observations}$$
23 = $$\frac {Sum \, of \, the \, observations}{11}$$
Sum of the observations = 23 × 11
= 253

10. Find the number of observations if the sum of the observations is 37.4 and the mean of the observations is 6.23?
a) 9
b) 7
c) 6
d) 4

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

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