The document contains 37 multiple choice questions related to measures of central tendency. The questions cover topics like mean, median, mode, skewed distributions, and how to calculate and interpret various central tendency measures. They assess understanding of key concepts such as how the mean, median and mode are affected by the shape and symmetry of different distributions.

1. MCQs
(Measures of central tendency)
NADEEM UDDIN
ASSOCIATE PROFESSOR
OF STATISTICS
https://www.slideshare.net/NadeemUddin17
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2. 1- For a certain distribution, if 𝑥 − 15 = 0, then 𝑥 is equal to:
a. 15 b. 0 c. 100 d. 200
2- If 𝑥 = 50 and 𝑦 = 3𝑥 − 10, then the mean of is:
a. 140 b. 160 c. 10 d. 20
3- If the mean of 5 numbers is 6 then 𝑥 is:
a. 30 b. 36 c. 25 d. 0
4- Sum of the deviation of the values from their mean is:
a. Minimum b. Zero c. Range d. Mode
5- The sum of the squares of the deviations of the values of a variable form their
mean is:
a. Minimum b. Maximum c. Zero d. Range

3. 6- The most frequent value of a data is:
a. Mean b. Median c. Mode d. Range
7- A distribution with one mode is called:
a. Mean b. Bimodal c. Multimodal d. Unimodal
8- A distribution with two modes is called:
a. Bimodal b. Unimodal c. Multimodal d. Median
9- A distribution with more than two modes is called:
a. Multimodal b. Unimodal c. Bimodal d. Mode
10- The symbol of sample mean is:
a. 𝑥 b.µ c. 𝑥 d. 𝑥

4. 11- The symbol of population mean is:
a. µ b. 𝑥 c. 𝑥 d. 𝑥
12- Mode of the series 2, 2, 3, 3, 4, 4, 4, 7, 9, 10 is:
a. 2 b. 4 c. 3 d. Zero
13- The sample mean 𝑥 is a:
a. Sample b. Parameter c. Statistic d. Population
14- The population mean µ is a:
a. Population b. Statistic c. Sample d. Parameter
15- The mean of series 7, 7, 7, 7, 7, 7 is:
a. 7 b. 42 c. Zero d. None

5. 16- We must arrange the data before calculating:
a. Mean b. Median c. Mode d. Range
17- Median is that value which divide the data into:
a. Four equal parts b. Three equal parts
c. Two equal parts d. None
18- Median of a series 2, 3, 4, 5, 6, 7 is:
a. 4.5 b. 4 c. 5 d. None
19- In a symmetrical distribution mean, median and mode are:
a. 𝑥 = 𝑥 = 𝑥 b. 𝑥 > 𝑥 > 𝑥 c. 𝑥 < 𝑥 < 𝑥 d. None
20- In a positively skewed distribution mean, median and mode are:
a. 𝑥 = 𝑥 = 𝑥 b. 𝑥 > 𝑥 > 𝑥 c. 𝑥 < 𝑥 < 𝑥 d. None

6. 21- In a negatively skewed distribution mean, median and mode are:
a. 𝑥 = 𝑥 = 𝑥 b. 𝑥 > 𝑥 > 𝑥 c. 𝑥 < 𝑥 < 𝑥 d. None
22- A curve that tail off two the right end is called:
a. Positively skewed b. Negatively skewed
c. Symmetrical d. None
23- A curve that tails off to the left end, is called:
a. Negatively skewed b. Positively skewed
c. Symmetrical d. None
24- If the mean, median and mode coincide in a unimodal distribution, then the
distribution will be:
a. Positively skewed b. Symmetrical
c. Negatively skewed d. None

7. 25- In a moderately skewed distribution, mean = 40 and median = 30, then the mode
is:
a. 10 b. 20 c. 90 d. 80
26- A data set contains the observations5, 1, 3, 2, 1 find 𝑥
a. 10 b. 20 c. 90 d. 12
27- The G.M of 2 and 8 is
a. 4 b. 20 c. 90 d. 12
28- An average monthly production of a certain factory for the first 9 months is 2584
units and for the remaining three months it is 2416 units find average monthly
production.
a. 4000 b. 2542 c. 900 d. 1250

8. 29- The average wage of 4 men is Rs. 17 per week. What is the average wage of
further 6 men if the average wage of all 10 men is Rs. 20.
a. 22 b. 20 c. 90 d. 12
30.- An examination candidate’s percentages are: English 73, Urdu 82; Mathematics
75; Science 62; History 60. Find the candidate’s weighted mean if weights of 4,
3, 3, 1,1 respectively are allotted to the subjects.
a. 40% b. 20% c. 90% d. 69.25%
31- If X1 = 11, X2 = 3, X3 = 4, X4 = 5, Evaluate. 𝑥 − 1 2
a. 22 b. 20 c. 90 d. 29
32- The formula u = x + 20 is used to find Mean of x it is found that
𝑓𝑖 = 40, 𝑢𝑖 𝑓𝑖 = 112
a. -17.2 b. - 20 c. 2.8 d. 29

9. 33- Find 𝑥 given that 𝑖=1
20
𝑥𝑖 = 226
a. 226 b. 11.3 c. 90 d. 20
34- Find 𝑦 given that 𝑖=1
20
𝑦𝑖 − 100 = 226
a. 100 b. 200 c. 111.3 d. 20
35- The numbers 3.2, 5.8, 7.9 and 4.5 have frequencies x, (x + 2), (x – 3) and (x + 6)
respectively if their mean is 4.876 find the value of x.
a. 3 b. 5 c. 4 d. 3.5

10. 36- If the average mark of 100 students is 28. Find missing value A and B.
Marks
No. of
students
0-10 A
10-20 18
20-30 27
30-40 20
40-50 B
50-60 6
a. A=12, B=17 b. A=10, B=20
c. A=1, B=2 d. None of these
37- The mean mark of 100 students was given to be 40. It was found later that a
mark 53 read as 83. What is the corrected mean mark?
a. 39.7 b. 40
c. 40.8 d. 38

11. 1-a 6-c 11-a 16-b 21-c 26-d 31-d 36-a
2-a 7-d 12-b 17-c 22-a 27-a 32-a 37-a
3-a 8-a 13-c 18-a 23-a 28-b 33-b
4-b 9-a 14-d 19-a 24-b 29-a 34-c
5-a 10-a 15-a 20-b 25-a 30-d 35-b
Answers