The following number of goals were scored by a team in a series

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 Multiple Choice QuestionsShort Answer Type

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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.


(i) Mean

 Mean equals fraction numerator Sum space of space all space the space observation over denominator Total space number space of space observation end fraction

           equals fraction numerator 2 plus 3 plus 4 plus 5 plus 0 plus 1 plus 3 plus 3 plus 4 plus 3 over denominator 10 end fraction
equals space 28 over 10 equals 2.8

(ii) Median

Arranging the given data in ascending order, we have
0, 1, 2, 3, 3, 3, 3, 4, 4, 5
Number of observations (n) = 10, which is even.

therefore   Median

equals fraction numerator open parentheses begin display style straight n over 2 end style close parentheses to the power of th observation plus open parentheses begin display style straight n over 2 end style plus 1 close parentheses to the power of th observation over denominator 2 end fraction
equals fraction numerator open parentheses begin display style straight n over 2 end style close parentheses to the power of th observation plus open parentheses begin display style 10 over 2 end style plus 1 close parentheses to the power of th observation over denominator 2 end fraction
equals space fraction numerator 5 to the power of th observation plus 6 to the power of th space observation over denominator 2 end fraction
equals fraction numerator 3 plus 3 over denominator 2 end fraction equals 6 over 2 equals 3

(iii) Mode
Arranging the given data in ascending order, we have
0, 1, 2, 3, 3, 3, 3, 4, 4, 5
Here, 3 occurs most frequently (4 times)
∴ Mode = 3.

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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.

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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

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59.

Find the mean of the following data:

x

f

10

3

12

10

20

15

25

7

35

5

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60.

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

Salary per worker (in र)

No. of workers

300

17

400

13

500

11

600

9

700

6

800

4

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