Vidaara.orgClass 11 · Mathematics
CodeVID-M11-WS
Measures of Central Tendency — Practice Worksheet
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Choose the correct option (A, B, C or D) for each question.
- The answer key is at the end — try the paper first!
Section A — Multiple Choice (1 mark each)
15 × 1 = 15 marks
1.
A single value that represents the whole data is a measure of:
- A.Dispersion
- B.Central tendency
- C.Correlation
- D.Frequency
2.
The arithmetic mean is found by:
- A.ΣX ÷ N
- B.Middle value
- C.Most frequent value
- D.Highest − lowest
3.
The arithmetic mean of 10, 20, 30, 40 is:
- A.20
- B.25
- C.30
- D.100
4.
The weighted mean is calculated as:
- A.ΣWX ÷ ΣW
- B.ΣX ÷ N
- C.ΣW ÷ ΣX
- D.ΣX × ΣW
5.
The biggest drawback of the arithmetic mean is that it is:
- A.Affected by extreme values
- B.Hard to define
- C.Never representative
- D.Always negative
6.
The middle value of ordered data is the:
- A.Mean
- B.Median
- C.Mode
- D.Range
7.
For an odd number N of values, the median is the value at position:
- A.N ÷ 2
- B.(N+1) ÷ 2
- C.N − 1
- D.2N
8.
The median of 2, 4, 6, 8 (even N) is:
- A.4
- B.5
- C.6
- D.20
9.
The median is NOT affected by:
- A.Extreme values
- B.The middle position
- C.Ordering
- D.The data
10.
The most frequently occurring value is the:
- A.Mean
- B.Median
- C.Mode
- D.Range
11.
The mode of 1, 2, 2, 3, 3, 3, 4 is:
- A.1
- B.2
- C.3
- D.4
12.
Which average can be found even for qualitative data (e.g. popular colour)?
- A.Mean
- B.Mode
- C.Geometric mean
- D.Weighted mean
13.
For a symmetrical distribution, mean, median and mode are:
- A.Equal
- B.Always different
- C.Zero
- D.Negative
14.
The empirical relation among the averages is:
- A.Mode = 3 Median − 2 Mean
- B.Mean = Mode + Median
- C.Median = Mean × Mode
- D.Mode = Mean ÷ 2
15.
To find the average income where a few people earn very high amounts, the best average is the:
- A.Mean
- B.Median
- C.Sum
- D.Range
Section B — Challenge / Olympiad (2 marks each)
10 × 2 = 20 marks
16.
Five workers earn ₹200, ₹250, ₹300, ₹350 and ₹3900. Why does the mean (₹1000) mislead here?
- A.One extreme value (₹3900) pulls the mean far above the typical wage
- B.The mean is always wrong
- C.There are too few values
- D.Wages cannot be averaged
17.
For the wages in the previous question, the median is:
- A.₹300
- B.₹1000
- C.₹3900
- D.₹250
18.
A subject with 4 credits scores 70 and a subject with 1 credit scores 95. The weighted mean is:
- A.75
- B.82.5
- C.70
- D.95
19.
A shopkeeper wants to stock the most-demanded shirt size. The most useful average is the:
- A.Mode
- B.Mean
- C.Median
- D.Range
20.
A distribution has Mean = 50 and Mode = 44. Using the empirical relation, the median is about:
- A.48
- B.44
- C.50
- D.94
21.
For an income group given as 'above ₹1,00,000' (open-ended), the mean cannot be found, so we use the:
- A.Median
- B.Arithmetic mean
- C.Weighted mean
- D.Sum
22.
The mean is preferred for further statistical calculations mainly because it:
- A.Uses every value in the data
- B.Ignores extreme values
- C.Is always a whole number
- D.Needs no data
23.
Data 5, 5, 7, 9, 9 has two modes (5 and 9). Such a distribution is called:
- A.Bimodal
- B.Unimodal
- C.Symmetrical
- D.Open-ended
24.
If every value in a data set occurs exactly once, the data have:
- A.No mode
- B.One mode
- C.Two modes
- D.An infinite mode
25.
Adding ₹100 to every worker's wage raises the mean wage by:
- A.₹100
- B.₹0
- C.depends on N
- D.₹100 × N
Answer Key
Section A — Multiple Choice (1 mark each)
- (B) Central tendency
- (A) ΣX ÷ N
- (B) 25
- (A) ΣWX ÷ ΣW
- (A) Affected by extreme values
- (B) Median
- (B) (N+1) ÷ 2
- (B) 5
- (A) Extreme values
- (C) Mode
- (C) 3
- (B) Mode
- (A) Equal
- (A) Mode = 3 Median − 2 Mean
- (B) Median
Section B — Challenge / Olympiad (2 marks each)
- (A) One extreme value (₹3900) pulls the mean far above the typical wage
- (A) ₹300
- (A) 75
- (A) Mode
- (A) 48
- (A) Median
- (A) Uses every value in the data
- (A) Bimodal
- (A) No mode
- (A) ₹100
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