Prepare discrite grouped frequency for
following data
4.4, 7.7 9.9, 8.8 9.9, 11, 8.86.5, 76,
36.3, 16.5, ss. 3, 89.7 38.5, 18 20
19.8 27.5, 308, 35,2 47.3, 82,3 39.8
42.9, 26, 4, 8462 40.7 49.5 30
20.9, 42.9, 31,9, 37.4,539,55,35.3,
37.4, 36,2,35.2, 19.8
Answers
Answer:
(A) Main Concepts and Results
Statistics
Meaning of ‘statistics’, Primary and secondary data, Raw/ungrouped data, Range of
data, Grouped data-class intervals, Class marks, Presentation of data - frequency
distribution table, Discrete frequency distribution and continuous frequency distribution.
• Graphical representation of data :
(i) Bar graphs
(ii) Histograms of uniform width and of varying widths
(iii) Frequency polygons
• Measures of Central tendency
(a) Mean
(i) Mean of raw data
Mean = 1 2 1 ...
n
i
n i
x
xx x
x
n n
+ ++ = = =
where x1
, x2
, ..., xn
are n observations.(ii) Mean of ungrouped data
i i
i
f x
x
f =
where f
i
’s are frequencies of xi
’s.
(b) Median
A median is the value of the observation which divides the data into two equal parts,
when the data is arranged in ascending (or descending) order.
Calculation of Median
When the ungrouped data is arranged in ascending (or descending) order, the median
of data is calculated as follows :
(i) When the number of observations (n) is odd, the median is the value of the
1
2
th n + observation.
(ii) When the number of observations (n) is even, the median is the average or
mean of the
2
th n
and 1
2
th n
+ observations.
(c) Mode
The observation that occurs most frequently, i.e., the observation with maximum
frequency is called mode. Mode of ungrouped data can be determined by observation/
inspection.
Probability
• Random experiment or simply an experiment
• Outcomes of an experiment
• Meaning of a trial of an experiment
• The experimental (or empirical) probability of an event E (denoted by P(E))
is given by
P(E) =
Number of trials in which the event has happened
Total number of trials
• The probability of an event E can be any number from 0 to 1. It can also be
0 or 1 in some special cases.
16/04/18(B) Multiple Choice Questions
Write the correct answer in each of the following :
Sample Question 1: The marks obtained by 17 students in a mathematics test (out of
100) are given below :
91, 82, 100, 100, 96, 65, 82, 76, 79, 90, 46, 64, 72, 68, 66, 48, 49.
The range of the data is :
(A) 46 (B) 54 (C) 90 (D) 100
Solution : Answer (B)
Sample Question 2: The class-mark of the class 130-150 is :
(A) 130 (B) 135 (C) 140 (D) 145
Solution : Answer (C)
Sample Question 3 : A die is thrown 1000 times and the outcomes were recorded as
follows :
Outcome 1 2 3 456
Frequency 180 150 160 170 150 190
If the die is thrown once more, then the probability that it shows 5 is :
(A)
9
50 (B)
3
20 (C)
4
25 (D)
7
25
Solution : Answer (B)
EXERCISE 14.1
Write the correct answer in each of the following :
1. The class mark of the class 90-120 is :
(A) 90 (B) 105 (C) 115 (D) 120
2. The range of the data :
25, 18, 20, 22, 16, 6, 17, 15, 12, 30, 32, 10, 19, 8, 11, 20 is
(A) 10 (B) 15 (C) 18 (D) 26
3. In a frequency distribution, the mid value of a class is 10 and the width of the class
is 6. The lower limit of the class is :
(A) 6 (B) 7 (C) 8 (D) 12
16/04. The width of each of five continuous classes in a frequency distribution is 5 and the
lower class-limit of the lowest class is 10. The upper class-limit of the highest class is:
(A) 15 (B) 25 (C) 35 (D) 40
5. Let m be the mid-point and l be the upper class limit of a class in a continuous
frequency distribution. The lower class limit of the class is :
(A) 2m + l (B) 2m – l (C) m – l (D) m – 2l
6. The class marks of a frequency distribution are given as follows :
15, 20, 25, ...
The class corresponding to the class mark 20 is :
(A) 12.5 – 17.5 (B) 17.5 – 22.5 (C) 18.5 – 21.5 (D) 19.5 – 20.5
7. In the class intervals 10-20, 20-30, the number 20 is included in :
(A) 10-20 (B) 20-30
(C) both the intervals (D) none of these intervals
8. A grouped frequency table with class intervals of equal sizes using 250-270
(270 not included in this interval) as one of the class interval is constructed for the
following data :
268, 220, 368, 258, 242, 310, 272, 342,
310, 290, 300, 320, 319, 304, 402, 318,
406, 292, 354, 278, 210, 240, 330, 316,
406, 215, 258, 236.
The frequency of the class 310-330 is:
(A) 4 (B) 5 (C) 6 (D) 7
9. A grouped frequency distribution table with classes of equal sizes using 63-72
(72 included) as one of the class is constructed for the following data :
30, 32, 45, 54, 74, 78, 108, 112, 66, 76, 88,
40, 14, 20, 15, 35, 44, 66, 75, 84, 95, 96,
102, 110, 88, 74, 112, 14, 34, 44.
The number of classes in the distribution will be :
(A) 9 (B) 10 (C) 11 (D) 12
10. To draw a histogram to represent the following frequency distribution :
Class interval 5-10 10-15 15-25 25-45 45-75
Frequency 6 12 10 8 15
16/04/18
Step-by-step explanation: