Chapter 14
Statistics
Exercise 14.2
Q1. The blood groups of 30 students of Class VIII are recorded as follows:
A,B,O,O,AB,O,A,O,B,A,O,B,A,O,O,A,AB,O,A,A,O,O,
AB,B,A,O,B,A,B,O
Represent this data in the form of a frequency distribution table. Which is the most common, and which is the rarest, blood group among these students?
Sol. :
|
Blood group
|
Number of students
|
|
A
|
09
|
|
B
|
06
|
|
O
|
12
|
|
AB
|
03
|
|
Total
|
30
|
Answer:
The most common O, and the Rarest AB blood group.
Q2. The distance (in Km) of 40 engineers from their residence to their place of work were found as follows:
5, 3, 10, 20, 25, 11, 13, 7, 12, 31, 19, 10, 12, 17, 18, 11, 32, 17, 16, 2,
7, 9, 7, 8, 3, 5, 12, 15, 18, 3, 12, 14, 2, 9, 6, 15, 15, 7, 6, 12
Construction a grouped frequency distribution table with class size 5 for the data given above taking the first interval as 0-5 (5 not included). What main features do you observe from this tabular representation?
Sol. :
|
Distance ( in Km)
|
Tally Marks
|
Frequency
|
|
00-05
|
//// |
05
|
|
05-10
|
//// //// /
|
11
|
|
10-15
|
//// //// /
|
11
|
|
15-20
|
//// /////
|
09
|
|
20-25
|
/
|
01
|
|
25-30
|
/
|
01
|
|
30-35
|
//
|
02
|
|
Total
|
|
40
|
Answer:
Most of the engineers live distance range 5-10, and 10-15km while least number of the engineers live distance rang 20-25, and 25-30km.
Q3. The relative humidity (in %) of certain city for a month of 30 days was as follows:
98.1, 98.6, 99.2, 90.3, 86.5, 95.3, 92.9, 96.3, 94.2, 95.1, 89.2, 92.3, 97.1,
93.5, 92.7, 95.1, 97.2, 93.3, 95.2, 97.3, 96.2, 92.1, 84.9, 90.2, 95.7, 98.3,
97.3, 96.1, 92.1, 89
i) Construct a grouped frequency distribution table with classes 84-86, 86-88, etc.
ii) Which month or season do you think this data is about?
iii) What is the range of this data?
Sol. :
i)
|
Relative humidity (in %)
|
Tally Marks
|
Frequency
|
|
84-86
|
/
|
1
|
|
86-88
|
/
|
1
|
|
88-90
|
//
|
2
|
|
90-92
|
//
|
2
|
|
92-94
|
//// //
|
7
|
|
94-96
|
//// /
|
6
|
|
96-98
|
//// /
|
7
|
|
98-100
|
////
|
4
|
|
Total
|
|
30
|
ii) The data appears to be taken in the rainy season as the relative humidity is high.
iii) Range 99.2-84.9=14.3.
Q4. The heights of 50 students, measured to the nearest centimetres, have been found to be as follows:
161, 150, 154, 165, 168, 161, 154, 162, 150, 151, 162, 164, 171, 165, 158,
154, 156, 172, 160, 170, 153, 159, 161, 170, 162, 165, 166, 168, 165, 164,
154, 152, 153, 156, 158, 162, 160, 161, 173, 166, 161, 159, 162, 167, 168,
159, 158, 153, 154, 159
i) Represent the data given above by a grouped frequency distribution table, taking the class intervals as 160-165, 165-170, etc.
ii) What can you conclude about their heights from the table?
Sol. :
i)
|
Height (in cm)
|
Tally Marks
|
Frequency
|
|
150-155
|
//// //// //
|
12
|
|
155-160
|
//// ////
|
09
|
|
160-165
|
//// //// ////
|
14
|
|
165-170
|
//// ////
|
10
|
|
170-175
|
////
|
05
|
|
Total
|
|
50
|
ii) one conclusion that we can draw from the above table is that more than 50% of student are shorten than 165cm
Q5. A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of the certain city. The data obtained for 30 days is as follows:
0.03, 0.08, 0.08, 0.09, 0.04, 0.17, 0.16, 0.05, 0.02, 0.06, 0.18, 0.20, 0.11,
0.08, 0.12, 0.13, 0.22, 0.07, 0.08, 0.01, 0.10, 0.06, 0.09, 0.18, 0.11, 0.07,
0.05, 0.07, 0.01, 0.04
i) Make a grouped frequency distribution table for this data with class intervals as 0.00-0.04,
0.04-0.08, and so on.
ii) For how many days, was the concentration of sulphur dioxide more than 0.11 part per million?
Sol. :
i)
|
The concentration of Sulpher dioxide (in ppm)
|
Tally Marks
|
Frequency
|
|
0.00-0.04
|
////
|
4
|
|
0.04-0.08
|
//// ////
|
9
|
|
0.08-0.12
|
//// ////
|
9
|
|
0.12-0.16
|
//
|
2
|
|
0.16-0.20
|
////
|
4
|
|
0.20-0.24
|
//
|
2
|
|
Total
|
|
30
|
ii) The concentration of sulphur dioxide was more than 0.11ppm for 8 days.
Q6. Three coins were tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows:
0,1,2,2,1,2,3,1,3,0,1,3,1,1,2,2,0,1,2,1,3,0,0,1,1,2,3,2,2,0
Prepare a frequency distribution table for the data given above.
Sol. :
|
Number of Heads
|
Tally Marks
|
Frequency
|
|
0
|
//// /
|
06
|
|
1
|
//// ////
|
10
|
|
2
|
//// ////
|
09
|
|
3
|
////
|
05
|
|
Total
|
|
30
|
Q7. The value of π up to 50 decimal places is given below:
3.14159265358979323846264338327950288419716939937510
i) Make a frequency distribution of the digits from 0 to 9 after the decimal point.
ii) What are the most and the least frequently occurring digits?
Sol. :
i)
|
Digits
|
Tally Marks
|
Frequency
|
|
0
|
//
|
2
|
|
1
|
////
|
5
|
|
2
|
////
|
5
|
|
3
|
//// ///
|
8
|
|
4
|
////
|
4
|
|
5
|
////
|
5
|
|
6
|
////
|
4
|
|
7
|
////
|
4
|
|
8
|
////
|
5
|
|
9
|
//// ///
|
8
|
|
Total
|
|
50
|
ii) The most frequently digits are 3 and 9. The least occurring is 0.
Q8. Thirty children were asked about the number of hours they watched TV programmers in the previous week. The results were found as follows:
1,6,2,3,5,12,5,8,4,8,10,3,4,12,2,8,15,1,17,6,
3,2,8,5,9,6,8,7,14,12
i) Make the grouped frequency distribution table for this data taking class width 5 and one of the class intervals as 5-10.
ii) How many children watched television for 15 or more hours a week?
Sol. :
i)
|
Number of hours
|
Tally Marks
|
Frequency
|
|
0-5
|
//// ////
|
10
|
|
5-10
|
//// //// ///
|
13
|
|
10-15
|
////
|
05
|
|
15-20
|
//
|
02
|
|
Total
|
|
30
|
ii) 2 children.
Q9. A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:
2.6,3.0,3.7,3.2,2.2,4.1,3.5,4.5,3.5,2.3,3.2,3.8,3.2,4.6,3.7,
2.5,4.4,3.4,3.3,2.9,3.0,4.3,2.8,3.5,3.2,3.9,3.2,3.2,3.1,3.7,
3.4,4.6,3.8,3.2,2.6,3.5,4.2,2.9,3.6
Construct a grouped frequency distribution table for this data , using class intervals of size 0.5 starting from the interval 2-2.5.
Sol. :
|
Life of batteries (in years)
|
Tally Marks
|
Frequency
|
|
2.0-2.5
|
//
|
02
|
|
2.5-3.0
|
//// /
|
06
|
|
3.0-3.5
|
//// //// ////
|
14
|
|
3.5-4.0
|
//// //// /
|
11
|
|
4.0-4.5
|
////
|
04
|
|
4.5-5.0
|
///
|
03
|
|
Total
|
|
40
|
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