1. For which of these would you use a histogram to show the data:
(a) The number of letters for different areas in a postman’s bag.
(b) The height of competitors in an athletics meet.
(c) The number cassettes produced by 5 companies.
(d) The number of passengers boarding trains from 7.00 a.m. to 7.00 p.m. at a station.
Give a reason for each of the following.
Since histogram is graphical representation of data, if data, if data represented in the form of class interval.
Therefore, for case (b) and (d), we would use a histogram to show the data, because in these cases, data can be divided into class-intervals. In case (b), a group of competitions having different heights in athletics meets. In case (d), the number of passengers boarding trains in an interval of one hour at a station.
In case (b), a group of competitions having different heights in athletics meets. In case (d), the number of passengers boarding trains in an interval of one hour at a station.
In case (d), the number of passengers boarding trains in an interval of one hour at a station.
2. Shoppers who come to a grocery store are identified as: Boy (B), Man (M), Girl (G) or Women (W). The list given below gives the shoppers who had come in the morning time slot:
W W W G B W W M G G M M W W W W G B M W B G G M W W M M W W W M W B W G M W W W W G W M M W M W G W M G W M M B G G W
Construct a frequency distribution table using the tally marks. Sketch a bar graph to represent it.
The representation of the above data by bar graph is as follows:
3. The weekly salary (in Rs) of 30 workers in are:
830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840.
By referring the tally marks, make a frequency table with following intervals as 800 – 810 , 810 – 820 and so on.
The illustration of data by frequency distribution table by using the tally marks is as follows:
4. Construct a histogram for frequency table made for the data that is given in question 3 and solve the following questions.
(i) Which group has highest workers?
(ii) Tell the number of workers who earn Rs. 850/- and more?
(iii) Identify the number of workers who earn less than Rs. 850/-
Histogram of the above frequency distribution table is as follows:
(i) Highest number of workers are present in 830 – 840 group.
(ii) The workers who earn more than Rs. 850, these workers fall in the category of 880 – 890 or 850 – 860 or 860 – 870. Therefore, the number of workers who are earning more than 850 will be the sum of the numbers of these workers i.e., 1 + 3 + 1 +1 + 4 = 10
(iii) The workers are being paid less than Rs.850 are the number of workers who come under the category 840 – 850 or 800 – 810 or 820 – 830 or 810 – 820 .Therefore, the number of workers who paid less than 850 will be the sum of the numbers of all these categories i.e.,
3 + 2 + 1 + 9 + 5 = 20
5. The students of particular class watched their lecture on television for different number of hours during the holidays; the results represented through graph.
Calculate the following:
(i) What is the number of hours did the maximum number of students watch TV?
(ii) What is the number of students who watched TV for less than 4 hours?
(iii) What is the total number of students who spent more than 5 hours in watching TV?
(i) It can be observed from the graph, that the maximum number of students (i.e., 32) watched TV for 4 – 5 hours.
(ii) The number of students who watched TV for less than 4hours are the students who watched TV for 3 – 4 hours or 2 – 3 hours or 1 – 2 hours.
Therefore, the total number of students = 4 + 8 + 22 = 34
(iii) The number of students who watched TV for more than 5 hours falls in the following category 5 – 6 hours or 6 – 7 hours.
Therefore, Sum of the above category of students = 8 + 6 = 14