**The quantity of goods produced and costs incurred by a firm are tabulated below. Find the correlation coefficient using Karl Pearson's formula.**

__Question:__Quantity producedTotal cost1012020230303154042550510

**Options:**

A. | 0.85 | |

B. | 0.93 | |

C. | 0.97 | |

D. | 0.99 |

**Answer: Option D**

: D

XiYiX2iY2iXiYi1012010014400120020230400529004600303159009922594504042516001806251700050510250026010025500∑=150∑=1600∑=5500∑=607250∑=57750

r=N∑ni=1(XiYi)–(∑ni=1Xi)(∑ni=1Yi)√N∑ni=1X2i–(∑ni=1Xi)2√N∑ni=1Y2i–(∑ni=1Yi)2=4875070.71×690.11=0.999

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## More Questions on This Topic :

- 20
- 30
- 40
- 50

**Answer: Option B**

: B

Draw a line parallel to the y-axis through x=10 to intersect the line of best fit. Through this point, draw a line parallel to the x-axis to intersect the y-axis. It can be seen that this line cuts y-axis near 30. Hence the approximate value of y corresponding to x=10 is 30.

**Spearman's rank coefficient is used to understand the correlation between variables which can be clearly quantified. State true or false.**

__Question 3.__- True
- False
- 0.965
- 0.982

**Answer: Option B**

: B

False. Spearman’s Rank coefficient helps us understand the correlation between the variables which can’t be very meaningful and predominantly subjective. It is generally used to find the correlationin caseof qualitative variables.

**Spearman's rank coefficient can be used to answer the question:**

__Question 4.__Does the number of symptoms a patient has indicate a higher severity of illness?

- False
- True
- 0.97
- 0.99

**Answer: Option B**

: B

Spearman's rank coefficient helps to understand the type of correlation by looking at non-linear ranked data. Hence this question can be answered using the same.

- 0.878
- 0.925
- 0.965
- 0.982

**Answer: Option D**

: D

xyx−¯x(x−¯x)2(y−¯y)(y−¯y)2(x−¯x)(y−¯y)24−39−6361836−24−416849−11−1115100000061111111713243968173974921∑=28∑=112∑=55 ¯x=∑xn=357=5

¯y=∑yn=707=10 r=∑ni=1(xi−¯x)(yi−¯y)√∑ni=1(xi−¯x)2√∑ni=1(yi−¯y)2=55√28×112=5556=0.982

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