NDA 2014
Exam NDA
Year 2014
Subject Mathematics
Chapter Statistics NDA 2014 · Mathematics · Statistics
Paragraph : The number of telephone calls received in 245...
< s t r o n g > P a r a g r a p h : < / s t r o n g > T h e n u m b e r o f t e l e p h o n e c a l l s r e c e i v e d i n 245 s u c c e s s i v e o n e m i n u t e i n t e r v a l s a t a n e x c h a n g e i s g i v e n b e l o w i n t h e f o l l o w i n g f r e q u e n c y d i s t r i b u t i o n . < t a b l e c l a s s = " q x − m a t c h − l i s t q x − m a t c h − t a b l e " b o r d e r = " 1 " c e l l p a d d i n g = " 6 " c e l l s p a c i n g = " 0 " > < t r > < t d > N u m b e r o f < b r > c a l l s < / t d > < t d > 0 < / t d > < t d > 1 < / t d > < t d > 2 < / t d > < t d > 3 < / t d > < t d > 4 < / t d > < t d > 5 < / t d > < t d > 6 < / t d > < t d > 7 < / t d > < / t r > < t r > < t d > F r e q u e n c y < / t d > < t d > 14 < / t d > < t d > 21 < / t d > < t d > 25 < / t d > < t d > 43 < / t d > < t d > 51 < / t d > < t d > 40 < / t d > < t d > 39 < / t d > < t d > 12 < / t d > < / t r > < / t a b l e > < s t r o n g > Q u e s t i o n : < / s t r o n g > W h a t i s t h e m e a n o f t h e d i s t r i b u t i o n ? <strong>Paragraph :</strong>
The number of telephone calls received in 245 successive one minute intervals at an exchange is given below in the following frequency distribution.
<table class="qx-match-list qx-match-table" border="1" cellpadding="6" cellspacing="0"><tr><td>Number of<br>calls</td><td>0</td><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td></tr><tr><td>Frequency</td><td>14</td><td>21</td><td>25</td><td>43</td><td>51</td><td>40</td><td>39</td><td>12</td></tr></table>
<strong>Question :</strong>
What is the mean of the distribution? < s t ro n g > P a r a g r a p h :< / s t ro n g > T h e n u mb ero f t e l e p h o n ec a ll srece i v e d in 245 s u ccess i v eo n e min u t e in t er v a l s a t an e x c han g e i s g i v e nb e l o w in t h e f o ll o w in g f re q u e n cy d i s t r ib u t i o n . < t ab l ec l a ss = " q x − ma t c h − l i s tq x − ma t c h − t ab l e " b or d er = "1" ce llp a dd in g = "6" ce ll s p a c in g = "0" >< t r >< t d > N u mb ero f < b r > c a ll s < / t d >< t d > 0 < / t d >< t d > 1 < / t d >< t d > 2 < / t d >< t d > 3 < / t d >< t d > 4 < / t d >< t d > 5 < / t d >< t d > 6 < / t d >< t d > 7 < / t d >< / t r >< t r >< t d > F re q u e n cy < / t d >< t d > 14 < / t d >< t d > 21 < / t d >< t d > 25 < / t d >< t d > 43 < / t d >< t d > 51 < / t d >< t d > 40 < / t d >< t d > 39 < / t d >< t d > 12 < / t d >< / t r >< / t ab l e >< s t ro n g > Q u es t i o n :< / s t ro n g > Wha t i s t h e m e an o f t h e d i s t r ib u t i o n ? Options A 3.76 B 3.84 C 3.96 D 4.05
Step-by-step solution
< t a b l e c l a s s = " q x − m a t c h − l i s t q x − m a t c h − t a b l e " b o r d e r = " 1 " c e l l p a d d i n g = " 6 " c e l l s p a c i n g = " 0 " > < t r > < t d > x < / t d > < t d > f < / t d > < t d > f x < / t d > < / t r > < t r > < t d > 0 < / t d > < t d > 14 < / t d > < t d > 0 < / t d > < / t r > < t r > < t d > 1 < / t d > < t d > 21 < / t d > < t d > 21 < / t d > < / t r > < t r > < t d > 2 < / t d > < t d > 25 < / t d > < t d > 50 < / t d > < / t r > < t r > < t d > 3 < / t d > < t d > 43 < / t d > < t d > 129 < / t d > < / t r > < t r > < t d > 4 < / t d > < t d > 51 < / t d > < t d > 204 < / t d > < / t r > < t r > < t d > 5 < / t d > < t d > 40 < / t d > < t d > 200 < / t d > < / t r > < t r > < t d > 6 < / t d > < t d > 39 < / t d > < t d > 234 < / t d > < / t r > < t r > < t d > 7 < / t d > < t d > 12 < / t d > < t d > 84 < / t d > < / t r > < t r > < t d > \cline 2 − 3 < / t d > < t d > 245 < / t d > < t d > 922 < / t d > < / t r > < / t a b l e > <table class="qx-match-list qx-match-table" border="1" cellpadding="6" cellspacing="0"><tr><td>\boldsymbol{x}</td><td>\boldsymbol{f}</td><td>\boldsymbol{f x}</td></tr><tr><td>0</td><td>14</td><td>0</td></tr><tr><td>1</td><td>21</td><td>21</td></tr><tr><td>2</td><td>25</td><td>50</td></tr><tr><td>3</td><td>43</td><td>129</td></tr><tr><td>4</td><td>51</td><td>204</td></tr><tr><td>5</td><td>40</td><td>200</td></tr><tr><td>6</td><td>39</td><td>234</td></tr><tr><td>7</td><td>12</td><td>84</td></tr><tr><td>\cline { 2 - 3 }</td><td>245</td><td>922</td></tr></table> < t ab l ec l a ss = " q x − ma t c h − l i s tq x − ma t c h − t ab l e " b or d er = "1" ce llp a dd in g = "6" ce ll s p a c in g = "0" >< t r >< t d > x < / t d >< t d > f < / t d >< t d > fx < / t d >< / t r >< t r >< t d > 0 < / t d >< t d > 14 < / t d >< t d > 0 < / t d >< / t r >< t r >< t d > 1 < / t d >< t d > 21 < / t d >< t d > 21 < / t d >< / t r >< t r >< t d > 2 < / t d >< t d > 25 < / t d >< t d > 50 < / t d >< / t r >< t r >< t d > 3 < / t d >< t d > 43 < / t d >< t d > 129 < / t d >< / t r >< t r >< t d > 4 < / t d >< t d > 51 < / t d >< t d > 204 < / t d >< / t r >< t r >< t d > 5 < / t d >< t d > 40 < / t d >< t d > 200 < / t d >< / t r >< t r >< t d > 6 < / t d >< t d > 39 < / t d >< t d > 234 < / t d >< / t r >< t r >< t d > 7 < / t d >< t d > 12 < / t d >< t d > 84 < / t d >< / t r >< t r >< t d > \cline 2 − 3 < / t d >< t d > 245 < / t d >< t d > 922 < / t d >< / t r >< / t ab l e >
Mean
= 922 245 = 3.76 =\frac{922}{245}=3.76 = 245 922 = 3.76
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