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```Chapter 32: Statistics – Exercise 32.2

Statistics – Exercise – 32.2 – Q.1

xi
fi
Cum.Freq
|di| = |xi - 61|
fi|di|

58
15
15
3
45

59
20
35
2
40

60
32
67
1
32

61
35
102
0
0

62
35
137
1
35

63
22
159
2
44

64
20
179
3
60

65
10
189
4
40

66
8
197
5
40

N = 197

Total = 336

Corresponding value for median is 61

Statistics – Exercise – 32.2 – Q.2

We have to calculate mean deviation from the median. So, first we calculate the median.

x
f
cf
d = (x – med)
fd

0
14
14
4
56

1
21
35
3
63

2
25
60
2
50

3
43
103
1
43

4
51
154
0
0

5
40
194
1
40

6
39
233
2
78

7
12
245
3
36

245
366

we have N = 245 ⟹ N/2 = 122.5

The cumulative frequency just greater than N/2 is 154 and the corresponding value of x is 4.

Hence, Median = 4

Statistics – Exercise – 32.2 – Q.3

xi
fi
Cum fre
|di| = |xi - 13|
fi|di|

5
2
2
8
16

7
4
6
6
24

9
6
12
4
24

11
8
20
2
16

13
10
30
0
0

15
12
42
2
24

17
8
50
4
32

N = 50

Total = 136

Value corresponding to 25 is median = 13

Statistics – Exercise – 32.2 – Q.4(i)

xi
fi
fixi
|di| = |xi - 9|
fi|di|

5
8
40
4
32

7
6
42
2
12

9
2
18
0
0

10
2
20
1
2

12
2
24
3
6

15
6
90
6
36

26
Total = 234

Total = 88

Mean = 9

Statistics – Exercise – 32.2 – Q.4(ii)

x
f
xf
d = (x - mean)
fd

5
7
35
9
63

10
4
40
4
16

15
6
90
1
6

20
3
60
6
18

25
5
125
11
55

25
350
158

Statistics – Exercise – 32.2 – Q.4(iii)

x
f
xf
d = (x – mean)
fd

10
4
40
40
160

30
24
720
20
480

50
28
1400
0
0

70
16
1120
20
320

90
8
720
40
320

80
4000
180

Statistics – Exercise – 32.2 – Q.4(iv)

xi
fi
fixi
|di| = |xi - 21.65|
fi|di|

20
6
120
1.65
9.9

21
4
84
0.65
2.6

22
5
110
0.35
1.75

23
1
23
1.35
1.35

24
4
96
2.35
9.4

20
Total = 433

Total = 25

Mean = 21.65

Statistics – Exercise – 32.2 – Q.5

xi
fi
Cum. Freq
|di| = |xi - 30|
fi|di|

15
3
3
15
45

21
5
8
9
45

27
6
14
3
18

30
7
21
0
0

35
8
29
5
40

29

Total = 148

Median = 30

We have to calculate mean deviation from the median, So, first we calculate the median,

x
f
cf
d = (x-med)
fd

35
4
4
39
456

42
2
6
32
64

54
4
10
20
80

74
20
30
0
0

89
12
42
15
180

91
5
47
17
85

94
3
50
20
60

50
625

We have N = 50 ⟹ N/2 = 25

The cumulative frequency just greater than N/2 is 30 and the corresponding value of x is 74.

Hence, median = 74

xi
fi
Cum. Freq
|di| = |xi - 12|
fi|di|

10
2
2
2
4

11
3
5
1
3

12
8
13
0
0

14
3
16
2
6

15
4
20
3
12

20

Total = 25

Median = 12

```

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