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Statistics — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSStatistics5 Marks
Question
Determine the mean and standard deviation for the following distribution:
Marks
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Frequency
1
6
6
8
8
2
2
3
0
2
1
0
0
0
1
✓

Answer

Marks
fi
fixi
$\text{d}_\text{i}=\text{x}_\text{i}-\bar{\text{x}}$
fidi
fidi2
2
1
2
-4
-4
16
3
6
18
-3
-18
54
4
6
24
-2
-12
24
5
8
40
-1
-8
8
6
8
40
-1
-8
8
7
2
14
1
2
2
8
2
16
2
4
8
9
3
27
3
9
27
10
0
0
4
0
0
11
2
22
5
10
50
12
1
12
6
6
36
13
0
0
7
0
0
14
0
0
8
0
0
15
0
0
9
0
0
16
1
16
10
10
100
Total
$\sum\text{f}_\text{i}=40$
$\sum\text{f}_\text{i}\text{x}_\text{i}=239$
 
$\sum\text{f}_\text{i}\text{d}_\text{i}=-1$
$\sum\text{f}_\text{i}\text{x}^2_\text{i}=325$
$\therefore\ \text{Mean }\bar{\text{x}}=\frac{\sum\text{f}_\text{i}\text{x}_\text{i}}{\sum\text{f}_\text{i}}=\frac{239}{40}=5.975\approx6$
and $\sigma=\sqrt{\frac{\sum\text{f}_\text{i}\text{x}_\text{i}}{\sum\text{f}_\text{i}}-\Big(\frac{\sum\text{f}_\text{i}\text{d}_\text{i}}{\sum\text{f}_\text{i}}\Big)^2}$
$=\sqrt{\frac{325}{40}-\Big(\frac{-1}{40}\Big)^2}$
$=\sqrt{8.125-0.000625}$
$=\sqrt{8.124375}$
$=2.85$

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