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Math Assignment Ch14 Class X  Statistics
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Chapter: 14(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.
Assignment on Statistics
Solve the following questions
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 

X 
Y 
2 
3 
4 
2 
6 
3 
10 
1 
P+5 
2 
Class Interval 
Frequency 
020 
16 
2040 
f1 
4060 
25 
6080 
16 
80100 
f2 
100120 
10 
Total 
90 
5. If mean=50 then find f1 & f2. Ans: f1 =28 & f2 = 24
Class Interval 
Frequency 
020 
17 
2040 
f1 
4060 
32 
6080 
f2 
80100 
19 
Total 
120 
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 
9. Find arithmetic mean by using suitable method. Ans:196.8
Class Interval 
Frequency 
080 
22 
80160 
35 
160240 
44 
240320 
25 
320400 
24 
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 
11. Find mode. Ans:18
Class Interval 
Frequency 
05 
3 
510 
7 
1015 
15 
1520 
30 
2025 
20 
2530 
10 
3035 
5 
12. Find median. Ans: 40
Class Interval 
Frequency 
010 
5 
1030 
15 
3060 
30 
6080 
8 
8090 
2 
13. 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 
14. Find median. Ans:29.42
Class Interval 
Frequency 
110 
10 
1120 
21 
2130 
51 
3140 
45 
4150 
26 
15. 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 
16. If median =35 then find f1 & f2.
Ans: F1=35 & f2= 25
Class Interval 
Frequency 
010 
10 
1020 
20 
2030 
f1 
3040 
40 
4050 
f2 
5060 
25 
6070 
15 
Total 
170 
17. Find median ages. Ans: 35.76
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 
18. Calculate Mean, mode, median.
Ans : Median=52 , Mean= 51.63 & Mode = 53.33
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 
19. 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 
20. 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 
21. Mode of the following data is 45, find x and y ,given n= 50
Ans x=10, y = 2
Class Interval 
Frequency 
1020 
4 
2030 
8 
3040 
X 
4050 
12 
5060 
10 
6070 
4 
7080 
Y 
22. Find the unknown entries a, b, c, d, e, f in the following
distribution if total no. of students is 50
class interval 
frequency 
c.f. 
150155 
12 
a 
155160 
b 
25 
160165 
10 
c 
165170 
d 
43 
170175 
e 
48 
175180 
2 
f 
23. If mode = 24.5 and mean is 29.75 then find median by using empirical formula. [Ans: 28]
24. Find the mode and median of the data. Ans[Mode= 9.56, Median= 12.19]
Class Interval 
Frequency 
58 
40 
811 
90 
1114 
44 
1417 
58 
1720 
53 
2023 
10 
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Creative questions. Keep it up
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