Tips & Tricks to solve Statistics Questions
Questions in the Statistics section of the State exam are usually asked from the following topics:
- Common Statistics Terms (Mean, Median, Mode etc)
- Frequency Distribution
- Data Interpretation
We will now discuss the tips to prepare each of these statistics topics for the Combined Defence Services exam.
(A) Common Terms & Formulas of Statistics
1. Mean
It basically refers to the average of the given data set. If ‘x’ items are given in the question, then its 'mean' is given by:
Here, ‘n’ is the total number of items.
2. Median
It refers to the middle of the centremost value of the given data set, once it is order in either ascending or descending order. If ‘n’ is the total number of given data items then, the median is given by:
(a) For an odd-numbered data set,
(b) For an even-numbered data set,
3. Mode refers to the most commonly occurring value/ item of the given data set, i.e. the item with the highest frequency.
4. Variance
The variance of a given data set can be calculated by:
Again, ‘x’ represents the given item of the data set, n represents the total number of items and bar ‘x’ is the mean.
5. Standard Deviation
It is used to calculate the variation in the given sample. T can be calculated by:
(B) Frequency Distribution
Frequency distribution basically to the orderly arrangement of given data based on their number of outcomes (frequency or the number of times they appear in the dataset) for each given item sample data. There are some important components of a frequency distribution table. These are:
1. Class
The class basically refers to the interval in which the different items of a large data set can be grouped, based on their size.
2. Class Limit
It refers to the highest and the lowest value of each class in the given frequency table.
3. Class Frequency
Class frequency refers to the number of items/ observations, which come in a class interval.
4. Mean of Frequency Distribution
If ‘f’ refers to the frequency in each class and ‘n’ is the sum of all the frequencies, then, mean of frequency distribution can be given by:
Suppose 4 different grades, ‘A’, ‘B’, ‘C’, ‘D’ are awarded to 20 workers of an organisation as:
A, C, A, B, A, D, B, B, C, A, C, C, D, D, B, D, D, A, C, A
Now, frequency refers to the total number of times each grade is given. Frequency Distribution table of such a data can be represented as:
Grade | Frequency |
A | 6 |
B | 4 |
C | 5 |
D | 5 |
The Concept of the class is used when the given data is large and spread out.
Suppose, the marks scored by 25 candidates in a test out of 300 are given as:
24, 36, 125, 216, 111, 119, 88, 70, 92, 121, 130, 60, 45, 197, 144, 99, 78, 174, 189, 120, 81, 75, 100, 123, 82
Now, smallest value = 24 and highest value = 216
Let us assume a class interval (range of marks) of ‘40’
Mid value = (24 + 216)/ 2 = 120.
Number of class intervals = 120/40 = 3
So, minimum 3 class intervals will be there in its frequency distribution table, which can be represented as:
Class Interval of marks obtained | Frequency |
0-39 | 2 |
40-79 | 5 |
80-119 | 8 |
120-159 | 6 |
160-199 | 3 |
200-239 | 1 |
(C) Data Interpretation
Data Representation, as the name suggests, refers to the representation of the given data set in graphical form, which may be a pie chart, bar chart, line chart, tabular representation etc.
Students are required to perform the relevant operation, as mentioned in the question, by interpreting the data provided in the graph.
There are no fixed set of formulas to solve the questions of Data Representation. Questions are usually based on the calculation of average, percentage, ratio and other elementary concepts of mathematics for the given data.
Students must make sure that they note down the correct numerical value of the item from the graph for accurate calculation.
As already mentioned, the questions of statistics are quite easy to solve with sufficient understanding and practice. Let’s have a look at some of the statistics questions asked in the previous exams of CDS.
1. In the following table of inverse variation, what are the values of A, B and C respectively?
M | 15 | -6 | 2 | C |
N | -4 | A | B | 60 |
(a) 10, -30, -1
(b) 10, -1, 30
(c) -30, 10, -1
(d) -1, -30, 10
Solution:
The question clearly mentions that the table represents inverse variation, so,
M ∝ 1/N
or, MN = K (Constant)
Considering the data of first 2 columns,
15*(-4) = K
And, (-6) *A = K
Equating both these equations,
15*(-4) = (-6) *A
Thus, A = 10
Similarly,
(-6) *A = 2*B
(-6) *10 = 2*B
Thus, B = -30
And, 2*B = C*60
2* (-30) = C*60
So, C = -1
Thus, the correct answer will be (b).
2. A Pie Chart is drawn for the following data:
Sector | Percentage |
Agriculture and Rural Development | 12.9 |
Irrigation | 12.5 |
Energy | 27.2 |
Industry and Minerals | 15.4 |
Transport and Communication | 15.9 |
Social Services | 16.1 |
What is the angle (approximately) subtended by the Social Services Sector at the centre of the circle?
(a) 45^{o}(b) 46^{o}(c) 58^{o}(d) 98^{o}
Solution:
In the given question, you need to interpret the given tabular data in form of a pie chart.
Clearly, 100% corresponds to 360^{0}You need to calculate the approximate angle subtended by the Social Services sector at circle’s centre.
For 16.1% è 360^{0}/100* 16.1 = 57.96^{0 }= 58^{0}Thus, the correct answer will be (c).
3. If a variable takes discrete values a + 4, a – 3.5, a – 2.5, a – 3, a – 2, a + 0.5, a + 5 and a – 0.5 where a > 0, then the median of the data set is:
(b) a - 2.5
(b) a - 1.25
(c) a - 1.5
(d) a - 0.75
Solution:
Arranging the values in ascending order, we get:
a - 3.5, a - 3, a - 2.5, a - 2, a - 0.5, a + 0.5, a + 4, a + 5
Since there are 8 values, the median of the set would be the average of the 4^{th} and 5^{th}values
Median= [(a - 2) + (a - 0.5)]/ 2
=a - 1.25
4. The arithmetic mean of 100 numbers was computed as 89.05. It was later found that two numbers 92 and 83 have been misread as 192 and 33 respectively. What is the correct arithmetic mean of the numbers?
(A) 88.55
(B) 87.55
(C) 89.55
(D) Cannot be calculated from the given data
Solution:
The Correct ‘arithmetic mean’ of the numbers is:
Hence Option (a) is correct.
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