9th Class Mathematics Unit 12 Information Handling Numericals with Solutions

12.1.1.The following distribution represents the scores achieved by a group of chemistry students in the chemistry laboratory. Scores: 24–28, 29–33, 34–38, 39–43, 44–48, 49–53 with No. of students: 3, 6, 12, 23, 15, 6 (Total 65). Answer the following questions. (i) What is the upper limit of the last class? (ii) What is the lower limit of the class 39–43? (iii) What is the midpoint of the class (34–38)? (iv) What are the class frequencies of the classes 29–33 and 44–48? (v) What is the size of the class limits in the above frequency distribution? (vi) In which class or group does minimum number of students fall? (vii) What is the lower limit of the class having 15 as its class frequency? (viii) What is the number of students having scores between 24 and 43?

Result

(i) Upper limit of last class 53

(ii) Lower limit of class 39-43 39

Formula

(iii) Midpoint Midpoint = frac{Lower class limit + Upper class limit{2}

Working

= 34+382 = 722

Result

= 36

(iv) Class frequencies of 29-33 and 44-48 6 and 15

(v) Size of class limits 5

(vi) Class with minimum students 24-28

(vii) Lower limit of class with frequency 15 44

Working

(viii) Students scoring between 24 and 43 3+6+12+23=44

12.1.2.For a school staff, the following expenditures (rupees in hundred) are required for the repair of chairs: 145, 152, 153, 156, 158, 160, 146, 152, 155, 159, 161, 163, 165, 147, 148, 151, 154, 156, 158, 160, 144, 167, 151, 150, 152, 149, 145, 153, 152, 155. Prepare a frequency distribution by tally bar method using 3 as the size of class limits and also write down what are the frequencies of the last three classes?

Given

Range Smallest value = 144, Largest value = 167

Frequency table (class width 3) 144-146:4, 147-149:3, 150-152:7, 153-155:5, 156-158:4, 159-161:4, 162-164:1, 165-167:2

Result

Total Sigma f = 30

Frequencies of last three classes 4, 1, 2

12.1.3.Given below are the weights in kg of 30 students of a high school: 30, 33, 24, 21, 15, 39, 37, 44, 42, 33, 33, 28, 29, 32, 31, 28, 26, 32, 34, 35, 38, 36, 41, 30, 35, 41, 23, 26, 18, 34. Taking 5 as the size of the class limit, prepare a frequency table and construct a frequency polygon.

Given

Range Smallest value = 15, Largest value = 44

Frequency table (class width 5) 15-19:2, 20-24:3, 25-29:5, 30-34:10, 35-39:6, 40-44:4

Result

Total and polygon Sigma f = 30

12.1.4.A group of Grade-10 students obtained the following marks out of 100 marks in English test: 58, 59, 58, 33, 40, 58, 45, 46, 43, 45, 45, 50, 52, 49, 50, 57, 52, 55, 49, 50, 62, 49, 48, 44, 42, 47, 46, 47, 46, 53, 40, 44. Classify the data into a frequency distribution by (direct method) taking 6 as the size of class limit. Also find the class limit with least class frequency and construct histogram for the data.

Frequency table (class width 6, direct method) 33-38:1, 39-44:6, 45-50:15, 51-56:4, 57-62:6

Result

Total Sigma f = 32

Histogram Class boundaries 32.5, 38.5, 44.5, 50.5, 56.5, 62.5

12.1.5.From the table given below, draw a frequency polygon on histogram for the given frequency distribution. Weight (kg): 10–14, 15–19, 20–24, 25–29, 30–34, 35–39 with Frequency (f): 06, 17, 23, 30, 22, 13.

Given

Class boundaries 9.5, 14.5, 19.5, 24.5, 29.5, 34.5, 39.5, 44.5

Result

Frequency polygon on histogram plotted using midpoints 12, 17, 22, 27, 32, 37

12.1.6.The following data shows the number of heads in an experiment of 50 sets of tossing a coin 5 times. Make a discrete frequency distribution from the information: 3, 3, 4, 0, 5, 4, 3, 3, 1, 2, 4, 5, 0, 3, 2, 4, 4, 0, 0, 0, 5, 5, 3, 2, 1, 4, 3, 2, 5, 3, 2, 1, 3, 5, 4, 3, 2, 1, 3, 2, 1, 3, 1, 3, 1, 4, 3, 2, 2, 4.

Tally of number of heads 0:5, 1:7, 2:9, 3:14, 4:9, 5:6

Result

Total Sigma f = 50

Unit 12: Information Handling — Exercise 12 1