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Statistics

Short 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
No. of balls	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

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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.

(i) Mean

   $equals fraction numerator 16 plus 18 plus 29 plus 31 plus 20 plus 23 plus 26 plus 25 plus 32 plus 20 over denominator 10 end fraction equals space 240 over 10 equals 24$

(ii) New mean

   $equals fraction numerator 240 minus 32 plus 23 over denominator 10 end fraction equals space 231 over 10 equals space 23.1$
(iii) Mean = 24 + 5 = 29

(iv) Mean of remaining 8 students

   $equals fraction numerator 240 minus left parenthesis 16 plus 32 right parenthesis over denominator 8 end fraction equals 192 over 8 equals 24$

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