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 `10-15 km` while least number of the engineers live distance rang `20-25,` and `25-30 km`.
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 `165 cm`
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 `0.11`ppm 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 `pi` 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`
|
Comments