## RS Aggarwal Solutions Chapter 14 Statistics Ex 14A in PDF for Free Download

Contents

**Question 1.****Define statistics as a subject.****Solution:**

Statistics is a science which deals with the collection, presentation, analysis and interpretations of numerical data.

**Question 2.****Define some fundamental characteristics of statistics.****Solution:**

(i) Numerical facts alone constitute data

(ii) Qualitative characteristics like intelligence, poverty etc. which cannot be measured, numerically, don’t form data.

(iii) Data are aggregate of facts. A single observation does not form data.

(iv) Data collected for a definite purpose may not be suited for another purpose.

(v) Data is different experiments are comparable.

**Question 3.****What are primary data and secondary data ? Which of the two is more reliable and why?****Solution:**

(i) Primary data : The data collected by the investigator himself with a definite plan in mind are called primary data.

(ii) Secondary data : The data collected by some one other than the investigator are called secondary data. The primary data is more reliable and relevant.

**Question 4.****Explain the meaning of each of the following terms :****(i) Variate****(ii) Class interval****(iii) Class size****(iv) Class mark****(v) Class limit****(vi) True class limits****(vii) Frequency of a class****(viii) Cumulative frequency of a class.****Solution:**

(i) Variate : Any character which is capable of taking several different values is called a variate or variable.

(ii) Class interval : Each group into which the raw data is condensed, is called a class interval

(iii) Class size : The difference between the true upper limit and the true lower limit of a class is called class size.

(iv) Class Mark : is called a class mark

(v) Class limits : Each class is bounded by two figures which are called class limits which are lower class limit and upper class limit.

(vi) True class limits : In exclusive form, the upper and lower limits of a class are respectively are the true upper limit and true lower limit but in inclusive form, the true lower limit of a class is obtained by subtracting O.S from lower limit of the class and for true limit, adding 0.5 to the upper limit.

(vii) Frequency of a class : The number of times an observation occurs in a class is called its frequency.

(viii) Cumulative frequency of a class : The cumulative frequency corresponding to a class is the sum of all frequencies upto and including that class.

**Question 5.****Following data gives the number of children in 40 families :****1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3,4, 2, 0, 4, 4, 3, 2, 2, 0, 0, 1, 2, 2, 4, 3, 2, 1, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2, 2.****Represent it in the form of a frequency distribution, taking classes 0-2, 2-4, etc.****Solution:**

The given data can be represent in form of frequency table as given below:

**Question 6.****The marks obtained by 40 students of a class in an examination are given below.****3, 20, 13, 1, 21, 13, 3, 23, 16, 13, 18, 12, 5, 12, 5, 24, 9, 2, 7, 18, 20, 3, 10, 12, 7, 18, 2, 5, 7, 10, 16, 8, 16, 17, 8, 23, 24, 6, 23, 15.****Present the data in the form of a frequency distribution using equal class size, one such class****being 10-15 (15 not included).****Solution:**

The frequency distribution table of the given data is given below :

**Question 7.****Construct a frequency table for the following ages (in years) of 30 students using equal class intervals, one of them being 9-12, where 12 is not included.****18, 12, 7, 6, 11, 15, 21, 9, 8, 13, 15, 17, 22, 19, 14, 21, 23, 8, 12, 17, 15, 6, 18, 23, 22, 16, 9,21,11,16.****Solution:**

The frequency distribution table of the

**Question 8.****Construct a frequency table with equal class intervals from the following data on the monthly wages-(in rupees) of 28 labourers working in a factory, taking one of the class intervals as 210-230 (230 not included).****220, 268, 258, 242, 210, 268, 272,242, 311, 200, 300, 320,’319, 304, 302, 318, 306, 292, 254,278,210,240,280,316,306,215,256,236.****Solution:**

The frequency table is given below :

**Question 9.****The weights (in grams) of 40 oranges picked at random from a basket are as follows****40, 50, 60, 65, 45, 55, 30, 90, 75, 85, 70, 85, 75, 80, 100, 110, 70, 55, 30, 35, 45, 70, 80, 85,95, 70, 60, 70, 75, 40, 100, 65, 60, 40, 100, 75, 110, 30, 45, 84.****Construct a frequency table as well as a cumulative frequency table.****Solution:**

The frequency table of given data is given below :

**Question 10.****The weekly wages (in rupees) of 30 workers in a factory are given below :****830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 836, 878, 840, 868, 890, 806, 840, 890.****Represent the data in the form of a frequency distribution with class size 10.****Solution:**

The frequency distribution table of the given data in given below :

**Question 11.****The electricity bills (in rupees) of 40 houses in a locality are given below :****116, 127, 107, 100, 80, 82, 91, 101, 65, 95, 87, 81, 105, 129, 92, 75, 89, 78, 87, 81, 59, 52, 65, 101, 115, 108, 95, 65, 98, 62, 84, 76, 63, 128, 121, 61, 118, 108, 116, 130.****Construct a grouped frequency table.****Solution:**

The frequency table of the given data given data :

**Question 12.****Following are the ages (in years) of 360 patients, getting medical treatment in a hospital:****Construct the cumulative frequency table for the above data.****Solution:**

The cumulative frequency of the given table is given below:

**Question 13.****Present the following as an ordinary grouped frequency table :****Solution:**

The given table can be represented in group frequency table in given below :

**Question 14.****Given below is a cumulative frequency table :****Extract a frequency table from the above.****Solution:**

Frequency table of the given cumulative frequency is given below :

**Question 15.****Make a frequency table from the following :****Solution:**

A frequency table of the given cumulative frequency table is given below :

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