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Statistics

Short Answer Type

51.

The following number of goals were scored by a team in a series of 10 matches :
2, 3, 4, 5, 0, 1, 3, 3, 4, 3
Find the mean, median and mode of these scores.

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52.
n a Mathematics test given to 15 students, the following marks (out of 100) are recorded :

41, 39, 48, 52, 46, 62, 54, 40, 96,
52, 98, 40, 42, 52, 60

Find the mean, median and mode of this data.

(i) Mean

Mean space equals space fraction numerator Sum space of space all space the space observation over denominator Total space number space of space observations end fraction equals fraction numerator 41 plus 39 plus 48 plus 52 plus 46 plus 62 plus 54 plus 40 plus 96 plus 52 plus 98 plus 40 plus 40 plus 52 plus 60 over denominator 15 end fraction equals 822 over 15 equals 54.8

(ii) Median
Arranging the given data in descending order, we have
98, 96, 62, 60, 54, 52, 52, 52, 48,
46, 42, 41, 40, 40, 39
Number of observations (n) = 15, which is odd.

$therefore space space space Median space equals space open parentheses fraction numerator straight n plus 1 over denominator 2 end fraction close parentheses to the power of th space observation. space space space space space space space space space space space space space space space space space space space equals open parentheses fraction numerator 15 plus 1 over denominator 2 end fraction close parentheses to the power of th space observation space$

= 8^th observation = 52

(iii) Mode

Arranging the data in descending order, we have
98, 96, 62, 60, 54, 52, 52, 52,
48, 46, 42, 41, 40, 40, 39
Here, 52 occurs most frequently (3 times)
∴ Mode = 52.

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53.

The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.

29, 32, 48, 50, x, x + 2, 72, 78, 84, 95

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54. Find the mode of 14, 25. 14, 28, 18, 17, 18, 14, 23, 22, 14. 18

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55.

Find the mean salary of 60 workers of a factory from the following table :

Salary (in Rs.)	Number of workers
3000	16
4000	12
5000	10
6000	8
7000	6
8000	4
9000	3
10000	1
Total	60

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56.

Give one example of a situation in which
(i) the mean is an appropriate measure of central tendency
(ii) the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.

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57.

Find the value of p if mean of following distribution is 20.

X	f
15	2
17	3
19	4
20 + p	5p
23	6

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58.

Find the mean $open parentheses top enclose x close parentheses$ of first ten prime numbers and hence show that $sum from straight i equals 1 to 10 of space left parenthesis x subscript i minus top enclose x right parenthesis equals 0$