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Math Assignment Ch13 Class X  Statistics
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Chapter: 13(Statistics)
Formulas used to solve the Assignment on statistics
Methods of finding mean in grouped data:
1. Direct
method :
2. Assumed mean method :
3. StepDeviation method :
Where, 

a 
Assumed mean 
di 
x_{i}a 
ui 
d_{i}/h or (x_{i}a)/h 
h 
height of C.I. 
Class mark=
Range = Highest value  Lowest value
Class size =
MODE of Data in Statistics
Mode: =
Where l = lower limit of the modal class,
h =
size of the class interval
f_{1} = frequency of the modal class
f_{0} = frequency of the class preceding the modal class,
f_{2} = frequency of the class succeeding the
modal class.
Median of Data in Statistics
Median: =
Median Class: Class corresponding to the is called median class
Where l= lower limit of median class
N = Sum of all observations
f = frequency of the median class.
Cf= cumulative
frequency of class preceding the median
class
h=
height of median class
Empirical Formula of Data in Statistics
Empirical Formula: Relation between mean, mode , median;
Mode=3 Median  2 Mean
Empirical formula does not
provide the same result in different situations. So, students should use it only when asked otherwise avoid it.
NOTE : For finding median, height of class interval need not to be equal or class interval may be irregular.
* If median class is the first class –interval then cumulative frequency (Cf) of the preceding class interval should be taken as zero.
* For finding Mean class interval need not to be continuous.
* For finding Mode and Median class interval should be continuous.
* For making class interval continuous we should subtract 0.5 from the lower limits and add 0.5 to the upper limits of all class intervals.
Assignment on Statistics
Solve the following questions
PROBLEMS BASED ON MEAN
Absent Students 
No. of days 
0 
1 
1 
4 
2 
10 
3 
50 
4 
34 
5 
15 
6 
4 
7 
2 
Total 
120 
Marks 
No. of Students 
010 
20 
1020 
24 
2030 
40 
3040 
36 
4050 
20 
Total 
14 0 
X 
Y 
2 
3 
4 
2 
6 
3 
10 
1 
P+5 
2 
Class Interval 
Frequency 
020 
16 
2040 
f_{1} 
4060 
25 
6080 
16 
80100 
f_{2} 
100120 
10 
Total 
90 
QUESTION 5. If mean=50 then find f_{1} & f_{2}. Ans: f_{1} =28 & f_{2} = 24
Class Interval 
Frequency 
020 
17 
2040 
f_{1} 
4060 
32 
6080 
f_{2} 
80100 
19 
Total 
120 
QUESTION 6. For the follwing data If mean =18 then find p. Ans: 1, 3
X 
Y 
13 
8 
15 
2 
17 
3 
19 
4 
20+p 
5p 
23 
6 
Class Interval 
Frequency 
110120 
2 
120130 
5 
130140 
11 
140150 
21 
150160 
26 
160170 
34 
170180 
36 
180190 
28 
190200 
16 
Do we use here stepdeviation method ? Why or Why not
Class Interval 
Frequency 
06 
11 
610 
10 
1014 
7 
1420 
4 
2028 
4 
2838 
3 
3840 
1 
No, we cannot use step deviation method here because height of the class intervals are not equal. So we can solve this question either by Direct Method or by Assumed mean method
Class Interval 
Frequency 
080 
22 
80160 
35 
160240 
44 
240320 
25 
320400 
24 
PROBLEMS BASED ON MODE
QUESTION 10. For the given data find mean & mode.
Ans : Mean=26 & Mode=22.85
Class Interval 
Frequency 
More than 0 
60 
More than 10 
56 
More than 20 
40 
More than 30 
20 
More than 40 
10 
More than 50 
3 
QUESTION 11. Find mode. Ans:18
Class Interval 
Frequency 
05 
3 
510 
7 
1015 
15 
1520 
30 
2025 
20 
2530 
10 
3035 
5 
QUESTION 12. Find mode. Ans:63.75
Height  No. of Plants 
More than 30  34 
More than40  30 
More than 50  27 
More than 60  19 
More than 70  8 
More than 80  2 
Class
Interval 
Frequency 
015 
10 
1530 
7 
3045 
x 
4560 
15 
6075 
10 
7590 
12 
Class Interval  Frequency 
1020  4 
2030  8 
3040  x 
4050  12 
5060  10 
6070  4 
7080  y 
PROBLEMS BASED ON MEDIAN
QUESTION 15. Find median. Ans: 40
Class Interval 
Frequency 
010 
5 
1030 
15 
3060 
30 
6080 
8 
8090 
2 
QUESTION 16. Find median. Ans:29.42
Class Interval 
Frequency 
110 
10 
1120 
21 
2130 
51 
3140 
45 
4150 
26 
QUESTION 17. If median=46 then find x & y. Ans: x = 33.5 & y = 45.5
Class Interval 
Frequency 
1020 
12 
2030 
30 
3040 
x 
4050 
65 
5060 
y 
6070 
25 
7080 
18 
Total 
229 
QUESTION 18. If median =35 then find f_{1} & f_{2}.
Ans: f_{1}=35 & f_{2}= 25
Class Interval 
Frequency 
010 
10 
1020 
20 
2030 
f_{1} 
3040 
40 
4050 
f_{2} 
5060 
25 
6070 
15 
Total 
170 
Ages 
No. of men 
Less than 20 
2 
Less than 25 
6 
Less than 30 
24 
Less than 35 
45 
Less than 40 
78 
Less than 45 
89 
Less than 50 
92 
Less than 55 
98 
Less than 60 
100 
QUESTION 20.
class interval  frequency  c.f. 
150155  12  a 
155160  b  25 
160165  10  c 
165170  d  43 
170175  e  48 
175180  2  f 
MISCELLANEOUS PROBLEMS ON MEAN, MODE, MEDIAN
QUESTION 21.
If mode = 24.5 and mean is 29.75 then find median by using empirical formula. [Ans: 28]
QUESTION 22.
Class Interval  Frequency 
58  40 
811  90 
1114  44 
1417  58 
1720  53 
2023  10 
QUESTION 23.
Calculate Mean, mode, median. Ans : Mean = 51.63, Mode = 53.33, Median = 52
QUESTION 23.
Calculate Mean, mode, median. Ans : Mean = 51.63, Mode = 53.33, Median = 52
Marks
No of
Students
More than
0
80
More than
10
76
More than
20
71
More than
30
65
More than
40
57
More than
50
43
More than
60
28
More than
70
15
More than
80
10
More than
90
8
More than
100
0
Marks 
No of
Students 
More than
0 
80 
More than
10 
76 
More than
20 
71 
More than
30 
65 
More than
40 
57 
More than
50 
43 
More than
60 
28 
More than
70 
15 
More than
80 
10 
More than
90 
8 
More than
100 
0 
HIGHER ORDER THINKING SKILLS (HOTS)
QUESTION 24. Find the missing frequency (f_{1}, f_{2}, and f_{3}) in the following data, when it is given that f_{2} : f_{3} = 4 : 3 and mean = 50
Answer: f_{1} = 28, f_{2} = 32 and f_{3} = 24
Class
Interval 
Frequency 
020 
17 
2040 
f_{1} 
4060 
f_{2} 
6080 
f_{3} 
80100 
19 
Total 
120 
Solution Hint: Use direct method to solve this question
For easy calculation use step deviation method and take
assume mean (a) in front of f_{1}
QUESTIONS DELETED FROM CBSE SYLLABUS
QUESTION 25. Find median by using less than ogive & actual calculation.
Ans: 27.5
Marks 
No. of Students 
Less than 10 
4 
Less than 20 
10 
Less than 30 
30 
Less than 40 
40 
Less than 50 
47 
Less than 60 
50 
QUESTION 26. Draw less than ogive & more than type ogive and find median. Ans:34.33
Class Interval 
Frequency 
010 
4 
1020 
8 
2030 
11 
3040 
15 
4050 
12 
5060 
6 
6070 
3 
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Creative questions. Keep it up
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