2 Marks Questions

Question 12 Marks

List some variables where accurate measurement is difficult.

Answer

The following are the some variables where the accurate measurement is difficult.
(i) Temperature and number of people falling ill.
(ii) Change in temperature with height of mountain
(iii) Low rainfall and agriculture productivity,
(iv) High population growth and degree of poverty
(v) Number of tourists and change in the political atmosphere in India.

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Question 22 Marks

In the given data set: 1, 2, 3, 4, 5; how many numbers are even or find the percentile ranking of even numbers?

Answer

Here, total numbers in given data set is 5, i.e., Y = 5 Also, there are two even numbers, (2 & 4) so here the value of M is 2.
Applying formula,
$P R=\frac{M}{Y} \times 100=\frac{2}{5} \times 100=40 \%$
Thus, there are 40% numbers in the given data set are even or we can say the percentile ranking of even number is 40%.

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Question 32 Marks

There are 5 students who go for medical checkup in a medical camp organized by a NGO. The medical score of the students are 5, 9, 4, 12, and 7. Identify the percentile rank for score 9.

Answer

Arrange the score data in ascending order:
4, 5, 7, 9, 12
using formula,
$P R=\frac{M}{Y} \times 100$
Here, Y = 5 and M = 4 ranking ordered score of 9)
$\therefore P R=\frac{4}{5} \times 100=0.8 \times 100=80 \%$
This concludes score 9 is higher than 80% of the scores.

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Question 42 Marks

Can r lie outside the -1 and +1 range depending on the type of data ?

Answer

No, the value of r cannot lie outside the range of -1 to +1. If r = -1, then there exists perfect negative correlation and if r = 1 then there exists perfect positive correlation between the two variables. If at any point of time the calculated value of r is outside this range, then there must be some mistake committed in the calculation.

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Question 52 Marks

For a group of 8 students, the sum of squares of differences in the ranks for mathematics and statistics marks was found to be 50. what is the value of rank correlation coefficient ?

Answer

As given, n = 8 and di² = 50 Hence, the rank correlation coefficient between Mathematics and statistics is given by marks in
$\begin{array}{l}r_s=1-\frac{6 \Sigma d^2}{n\left(n^2-1\right)}=1-\frac{6 \times 50}{8\left(8^2-1\right)}=1-\frac{300}{8 \times 63} \\ =\frac{504-300}{504}=0.40 .\end{array}$

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Question 62 Marks

Why r is preferred to covariance as a measure of association ?

Answer

Although correlation coefficient is similar to the covariance in a manner that both measure the degree of linear relationship between two variables, but the former is generally preferred to covariance due to the following reasons:
(i) The value of the correlation coefficient (r) lies between -1 and 1 i.e., $-1 \leq r \leq 1$
(ii) The correlation coefficient is scale free.

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Applied Maths 2 Marks Questions

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