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Statistics

Long Answer Type

521. The following is the record of goals scored by team A in a football session:

For team B, mean number of goals scored per match was 2 with a standard deviation 1.25 goals. Find which of the teams may be considered more consistent?

110 Views

Short Answer Type

522.

The means and standard deviation of heights and weights of 50 students of a class are as follows:
WEIGHTS (kg.) HEIGHT (inches)
Mean 63.2 63.2
S.D. 5.6 11.5
Which shows more variability, the highest or weights?

173 Views

Long Answer Type

523. From the data given below, state which group is more variable, A or B?

Group A

Mean =

straight A plus fraction numerator begin display style sum from blank to blank of end style f u over denominator straight N end fraction cross times i space equals space 45 plus fraction numerator negative 6 over denominator 150 end fraction cross times 10 space equals space 45 minus 0.4

rightwards double arrow

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...(i)

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equals 1 over 150 square root of left parenthesis 342 cross times 150 minus 36 right parenthesis end root space cross times space 10

equals space 1 over 15 square root of 51300 minus 36 end root space equals space 1 over 15 square root of 51264 space equals space 1 over 15 cross times 226.4

∴

straight sigma subscript 1 space equals space 15.1 space left parenthesis approx right parenthesis.

Group B

Mean =

straight A plus fraction numerator begin display style sum from blank to blank of end style f u over denominator straight N end fraction cross times space i space equals space 45 plus fraction numerator negative 6 over denominator 150 end fraction cross times 10 equals 44.6

Since, the means of the two datas are same, variability can be compared only through S.D.

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equals space square root of 366 over 150 minus open parentheses fraction numerator negative 6 over denominator 150 end fraction close parentheses squared end root space cross times space i space equals space 1 over 150 cross times square root of 366 cross times 150 minus 36 end root space cross times space 10

equals space 1 over 15 square root of 54900 minus 36 end root space equals space 1 over 15 cross times square root of 54864 space equals space 1 over 15 cross times 234 space left parenthesis approx. right parenthesis

∴

straight sigma subscript 2 space equals space 15.6 space left parenthesis approx. right parenthesis

straight sigma subscript 2 greater than straight sigma subscript 1

rightwards double arrow

The data for group B is more variable.

107 Views

Short Answer Type

524.

The marks scored by two students A and B in 8 tests during an academic session were : A (marks out of 100) 70, 79, 81, 68, 52, 57, 68, 85.
B (marks out of 100) 89, 72, 75, 91, 54, 51, 64, 64 Which of the two has more variability in marks?

105 Views

525.

Runs scored by two batsmen during cricket season, in 8 innings were as follows : A : 48, 56, 54, 39, 46, 59, 48, 50
B: 68, 84, 65, 83, 46, 20, 98, 96
Which of the batsmen is more consistent and which one is more invariable?

106 Views

526. The following values are calculated in respect of heights and weights of the students of a section of class XI.
Height Weight
Mean 162.6 cm 52.36 kg
Variance 127.69 cm² 23.1361 kg²Can we say that weight show greater variation than the height.

128 Views

527. The number of goals scored by team A in 20 matches of a tournament are as follow:
Number of goals scored 0 1 2 3 4
Number of Matches 0 2 9 6 3
Another team B scores at an average of 2.5 goals per match with a standard deviation. Find which of the two teams is more consistent?

109 Views

528. The mean and standard deviation of 100 students of a class in the subjects of English, Hindi and Social Studies are given below:
Subject Hindi English S.Studies
Mean 45 51 60
S.D. 9 12 15
Which of the three subjects is most consistent and which one is most variable?

105 Views

529. Which of the two datas given below is more consistent?
(A)
X 6 10 14 18 24 28 30
f 2 4 7 12 8 4 3

(B)
X 92 93 97 98 102 104 109
f 3 2 3 2 6 3 3

104 Views

530. The analysis of daily wages paid to workers in two firms A and B belonging to the same industry, are:

(i) Which Firm A or B pays more in total daily wages? (ii) Which firm A or B, shows greater variability in wages?

115 Views