MCQs on Mean

1.      The mean of a set of 50 observations was calculated as 42. It was discovered later that two items were recorded as 93 and 8 instead of 39 and 88. Rectify the error and find the correct mean.

Given n= 50 and X̅ =42.

Thus, ∑X = 42x50=2100 But this value is incorrect because of inclusion of two items wrongly

Corrected ∑X=2100-93-8+39+88= 2126

Corrected X̅= 2126/50=42.52

2.      An auto Riksha ride was Rs. 19 for the first two kilometres and Rs. 6.50 per km after that. The cost of each one tenth of kilometre is incurred in advance. What is the average cost per Kilometre to a passenger travelling 8.75 Kilometre.

Kilometer travelled 8.75 - 2 KM because of fixed rate Rs. 19/- remains 6.75 Km but one tenth km is added in advance so 6.80 Km travel and charges are 6.50 /- per kilometer. So total charges

                                            = 19 + 6.80x6.50= 63.20/ 8.75= 7.22 per km

He paid 63.20 and travelled 8.75 km so per km charges are Rs. 7.22 /- per km

Number of observations are 30 and value of arithmetic mean is 15 then sum of all values is

A.     15

B.     450

C.     200

D.     45

In arithmetic mean, sum of deviations of all recorded observations must always be

A.     two

B.     minus one

C.     one

D.     zero

Arithmetic mean is 25 and all sum of observations is 350 then number of observations are

25

70

14

75

Arithmetic mean is 12 and number of observations are 20 then sum of all values is

1. 8
2. 32
3. 240
4. 1.667

Answer C

  Arithmetic mean is multiplied to coefficient of mean absolute deviation to calculate the

1. absolute mean deviation
2. absolute median deviation
3. relative mean deviation
4. relative median deviation

In the following multiple choice questions, circle the correct answer.

1. A numerical value used as a summary measure for a sample, such as sample mean, is known as a

a. population parameter
b. sample parameter
c. sample statistic
d. population mean
e. None of the above answers is correct.

ANSWER: c

If it pertains to sample it is called a statistic, if it pertains to population it is called a parameter.

2. Since the population size is always larger than the sample size, then the sample statistic

a. can never be larger than the population parameter
b. can never be equal to the population parameter
c. can never be zero
d. can never be smaller than the population parameter
e. None of the above answers is correct.

ANSWER: e

Sample statistic will depend upon the sample chosen. It can be less than, greater than, equal to population parameter. It can assume the value of zero.

3.  is an example of a

a. population parameter
b. sample statistic
c. population variance
d. mode
e. None of the above answers is correct.

ANSWER: a

M is a standard representation for population parameter.

4. The mean of a sample is

a. always equal to the mean of the population
b. always smaller than the mean of the population
c. computed by summing the data values and dividing the sum by (n - 1)
d. computed by summing all the data values and dividing the sum by the number of items
e. None of the above answers is correct.

ANSWER: d

Mean= Total of sample values/ sample size

5. The sum of the percent frequencies for all classes will always equal

a. one
b. the number of classes
c. the number of items in the study
d. 100
e. None of the above answers is correct.

ANSWER: d

If we count the total frequency it is equal to the sample size n. n/n *100= 100

6. In a five number summary, which of the following is not used for data summarization?

a. the smallest value
b. the largest value
c. the median
d. the 25th percentile
e. the mean

ANSWER:d

7. Since the mode is the most frequently occurring data value, it

a. can never be larger than the mean
b. is always larger than the median
c. is always larger than the mean
d. must have a value of at least two
e. None of the above answers is correct.

ANSWER: e

The mean, median and mode values will be distributed according to the skewness of the distribution. Accordingly mode can be greater than or less than mean or mode.

Exhibit 1-1
The following data show the number of hours worked by 200 statistics students.

Number of Hours                   Frequency

 0 - 9                                        40
10 - 19                                     50
20 - 29                                     70
30 - 39                                     40

8. Refer to Exhibit 1-1. The class width for this distribution

a. is 9
b. is 10
c. is 11
d. varies from class to class
e. None of the above answers is correct.
ANSWER: b