The following observations have been arranged in ascending order

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 Multiple Choice QuestionsShort Answer Type

211. The mean of five observations x, x + 2, x + 4, x + 6 and x + 8 is 23. Find the mean of last four observations.
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212.

The runs scored by two teams A and B on the first 74 balls in a cricket match are given below:

No. of balls

Runs scored

Team A

Team B

0–12

10

4

12–24

12

2

24–36

4

16

36–48

20

18

48–60

10

8

60–72

12

10

72–84

6

12


Construct the frequency polygon for both teams on the same graph.
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213.

The distance (in 1 cm) covered by 30 cars in 2 hrs. are given below:

125, 107, 120, 90, 84, 100,
56, 140, 93, 149, 73, 68,
88,135,115,120,90,120,
136, 144, 104, 135, 60, 79
83, 100, 76,91,89, 120

Form a frequency distribution table (with tally works), one of the intervals being 100-120 (120 not included).

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214. Calculate mean of first 5 prime numbers.
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215.

Find the mean of the following distribution:

Variable (x)

Frequency (f)

4

12

5

10

6

8

7

7

8

8

9

5

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216.

The following observations have been arranged in ascending order. If the median of the data in 65, find the value of x.
32, 35, 50, 51, x, x + 2, 73, 76, 83, 90


Number of observation (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 space observation space 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
rightwards double arrow space 65 equals fraction numerator 5 to the power of rh space observation plus 6 to the power of th space observation over denominator 2 end fraction
rightwards double arrow space space 65 equals fraction numerator straight x plus left parenthesis straight x plus 2 right parenthesis over denominator 2 end fraction
rightwards double arrow space space 2 straight x plus 2 equals 130
rightwards double arrow space space 2 straight x equals 130 minus 2 equals 128
rightwards double arrow space space straight x equals 128 over 2 equals 64
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217.

Find the value of p, if the mean of the following distribution is 7.5:

x

y

3

6

5

8

7

15

9

8

11

8

13

4

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218. Find the mode of the data 15, 14, 19, 20,14,15,16,14,15,18,14,19,15,17,15. If last observation is changed to 14, then find the new mode.
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219. The mean of 200 items was 50. Later on, it was discovered that the two items were misread as 92 and 8 instead of 192 and 88. Find the correct mean. 
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220.

Marks secured by a group of 10 students are as follows:
16, 18, 29, 31, 20, 23, 26, 25, 32, 20
(i) Find the mean of the data,
(ii) If 32 is replaced by 23 in the data. find the new mean.
(iii) If each observation in the given data is increased by 5 marks, then what will be the mean?
(iv) If two students securing 16 and 32 leave the group, then find the mean of remaining 8 students.

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