Maths Statistics Exercise20-2
Please Select
Q1 State which of the following variables are continuous and which are discrete:
(i)marks scored (out of 50) in a test.
(ii) daily temperature of your city.
(iii) sizes of shoes.
(iv)distance travelled by a man.
(v)time.
Solution :
Q2 Using class intervals 0-4, 5 -9, 10-14, …. construct the frequency distribution for the following data :
13, 6, 10, 5, 11, 14, 2, 8, 15, 16, 9, 13, 17, 11, 19, 5, 7, 12, 20, 21, 18, 1, 8, 12, 18.
Solution :
Q3 Given below are the marks obtained by 27 students in a test:
21, 3, 28, 38, 6, 40, 20, 26, 9, 8, 14, 18, 20, 16, 17, 10, 8, 5, 22, 27, 34, 2, 35, 31, 16, 28, 37.
(i) Using the class intervals 1-10, 11-20 etc. construct a frequency table.
(ii) State the range of these marks.
(iii) State the class mark of the third class of your frequency table.
Solution :
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Q4 A Explain the meaning of the following terms :
(i) variate
(ii) class size
(iii) class mark
(iv) class limits
(v) true class limits
(vi) frequency of a class
(vii) cumulative frequency of a class.
Solution :
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Q5 Fill in the blanks :
(i) The number of observations in a particular class is called ……of the class.
(ii) The difference between the class marks of two consecutive classes is the of the class.
(iii) The range of the data 16, 19, 23, 13, 11, 25, 18 is.. .
(iv) The mid-point of the class interval is called its …
(v) The class mark of the class 4 – 9 is ….
Solution :
Q6 The marks obtained (out of 50) by 40 students in a test are given below:
28, 31, 45, 03, 05, 18, 35, 46, 49, 17, 10, 28, 31, 36, 40, 44, 47, 13, 19, 25, 24, 31, 38, 32, 27, 19, 25, 28, 48, 15, 18, 31, 37, 46, 06, 01, 20, 10, 45, 02.
(i) Taking class intervals 1- 10, 11 – 20, .., construct a tally chart and a frequency distribution table.
(ii) Convert the above distribution to continuous distribution.
(iii) State the true class limits of the third class.
(iv) State the class mark of the fourth class.
Solution :
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Q7 Use the adjoining table to find:
(i) upper and lower limits of fifth class.
(ii) true class limits of the fifth class.
(iii) class boundaries of the third class.
(iv) class mark of the fourth class.
(v) width of sixth class.
Solution :
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Q8 The marks of 200 students in a test were recorded as follows:
Draw the cumulative frequency table.
Solution :
Q9 Given below are the marks secured by 35 students in a test:
41, 32, 35, 21, 11, 47, 42, 00, 05, 18, 25, 24, 29, 38, 30, 04, 14, 24, 34, 44, 48, 33, 36, 38, 41, 46, 08, 34, 39, 11, 13, 27, 26, 43, 03.
Taking class intervals 0-10, 10-20, 20-30 …., construct frequency as well as cumulative frequency distribution table. Find the number of students obtaining below 20 marks.
Solution :
Q10 The marks out of 100 of 50 students in a test are given below:
5 35 6 35 18 36 12 36 85 32
20 36 22 38 24 50 22 39 74 31
25 54 25 64 25 70 28 66 58 25
29 72 31 82 31 84 31 82 37 21
32 84 32 92 35 95 34 92 35 5
(i) Taking a class interval of size 10, construct a frequency as well as cumulative frequency table for the given data.
(ii) Which class has the largest frequency?
(iii) How many students score less than 40 marks?
(iv) How many students score first division (60% or more) marks?
Solution :
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Q11 Construct the frequency distribution table from the following data:
State the number of children in the age group 10-13.
Solution :
Q12 Rewrite the following cumulative frequency distribution into frequency distribution:
Less than or equal to 10 2
Less than or equal to 20 7
Less than or equal to 30 18
Less than or equal to 40 32
Less than or equal to 50 43
Less than or equal to 60 50
Solution :
Q13 The water bills (in rupees) of 32 houses in a locality are given below. Construct a frequency distribution table with a class size of 10.
80, 48, 52, 78, 103, 85, 37, 94, 72, 73, 66, 52, 92, 85, 78, 81, 64, 60, 75, 78, 108, 63, 71, 54, 59, 75, 100, 103, 35, 89, 95, 73.
Solution :
Q14 The maximum temperatures (in degree Celsius) for Delhi for the month of April, 2014, as reported by the Meteorological Department, are given below:
27.4, 28.3, 23.9, 23.6, 25.4, 27.5, 28.1, 28.4, 30.5, 29.7, 30.6, 31.7, 32.2, 32.6, 33.4, 35.7, 36.1, 37.2, 38.4, 40.1, 40.2, 40.5, 41.1, 42.0, 42.1, 42.3, 42.4, 42.9, 43.1, 43.2.
Construct a frequency distribution table.
Solution :
Q15 (i) The class marks of a distribution are 94, 104, 114, 124, 134, 144 and 154. Determine the class size and the class limits of the fourth class.
(ii) The class marks of a distribution are 9.5, 16.5, 23.5, 30.5, 37.5 and 44.5. Determine the class size and the class limits of the third class.
Solution :
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