Question

The final marks in mathematics of $$30$$ students are as follows
$$53,61,48,60,78,68,55,100,67,90,75,88,77,37,84,58,60,48,62,56,44,58,52,64,98,59,70,39,50,60$$
arrange this marks in the ascending order 30 to 39 one group, 40 to 49 second group, etc
 i.What is the highest score?
 ii.What is the lowest score?
iii. What is the range?
iv. If $$40$$ is the pass mark how many have failed?
v. How many have scored $$75$$ or more?
vi. which observation between $$50$$ and $$60$$ have not actually appeared?
vii. How many have scored less than $$50$$ ?

Answer 1

Hint: We need to observe the data given in problem . After analyzing the data given in question we can solve the sub-question given in problem

Complete step-by-step answer:
The marks in the ascending order, 30 to 39 one group, 40 to 49 second group, etc are as follows :
$$\eqalign{
  & 1.\;\;\;\;\;\;\left( {30{\text{ }} - {\text{ }}39} \right){\text{ }} \to {\text{ }}\;37,{\text{ }}39 \cr
  & 2.\;\;\;\;\;\;\left( {40{\text{ }}-{\text{ }}49} \right){\text{ }} \to {\text{ }}44,{\text{ }}48,{\text{ }}48 \cr
  & 3.\;\;\;\;\;\;\left( {50{\text{ }}-{\text{ }}59} \right) \to \;50,{\text{ }}52,{\text{ }}53,{\text{ }}55,{\text{ }}56,{\text{ }}58,{\text{ }}58,{\text{ }}59 \cr
  & 4.\;\;\;\;\;\;\left( {60{\text{ }}-{\text{ }}69} \right){\text{ }} \to {\text{ }}60,{\text{ }}60,{\text{ }}60,{\text{ }}61,{\text{ }}62,{\text{ }}64,{\text{ }}67,{\text{ }}68 \cr
  & 5.\;\;\;\;\;\;\left( {70{\text{ }}-{\text{ }}79} \right) \to {\text{ }}70,{\text{ }}75,{\text{ }}77,{\text{ }}78 \cr
  & 6.\;\;\;\;\;\;\left( {80{\text{ }}-{\text{ }}89} \right) \to {\text{ }}84,{\text{ }}88 \cr
  & 7.\;\;\;\;\;\;\left( {90{\text{ }}-{\text{ }}99} \right) \to {\text{ }}90,{\text{ }}98 \cr
  & 8.\;\;\;\;\;\;\left( {100 - 109} \right){\text{ }} \to \;100 \cr} $$
(i) The highest score is $$100$$ .

(ii) The lowest score is $$37$$ .

(iii) Range = Maximum observation – Minimum observation.
    = 100-37
   =63
Hence , the range is $$63$$ .

(iv) If $$40$$ is the pass mark, then only $$2$$ students have failed.

(v) $$8$$ students have scored $$75$$ or more.

(vi) $$51,{\text{ }}54$$ and $$57$$ observations between $$50$$ and $$60$$ have not actually appeared.

(vii) $$5$$ students scored less than $$50$$ .

Note: Here we analyze the data. Data is unorganised raw facts that need processing without which it is seemingly random and useless to humans.