Std 7 Mathematics Chapter  15. Statistics

Title : Std 7 Mathematics Chapter  15. Statistics

Maharashtra state board solutions for class 7 SSC board maths  STD 7 Statistics

 Know everything about Statistics Maharashtra state board class 7 SSC .Get detailed Questions and answers for chapter5 maths.

Important questions and answers

Average

Average means constituting the result obtained by adding together several amounts and then dividing this total by the number of amounts. The ‘average’ is a useful figure in the study of all branches of science including medicine, geography, economics, social science, etc.

For Example : The average of 10,20,30,40,50 will be :

𝑆𝑢𝑚 𝑜𝑓 𝑎𝑙𝑙 𝑠𝑐𝑜𝑟𝑒𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑔𝑖𝑣𝑒𝑛 𝑑𝑎𝑡𝑎           =               10+20+30+40+50

𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑐𝑜𝑟𝑒𝑠                                                          5                              

 = 150

     5

 = 30

The samples that we have of the quantity we are measuring are called ‘readings’ or ‘scores’.

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 = 𝑆𝑢𝑚 𝑜𝑓 𝑎𝑙𝑙 𝑠𝑐𝑜𝑟𝑒𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑔𝑖𝑣𝑒𝑛 𝑑𝑎𝑡𝑎 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑐𝑜𝑟𝑒𝑠 2

*Q.1 Rutuja practised skipping with a rope all seven days of a week. The number of times she jumped the rope in one minute every day is given below. 60, 62, 61, 60, 59, 63, 58.

Solution : 𝑆𝑢𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑗𝑢𝑚𝑝𝑠 𝑜𝑛 𝑠𝑒𝑣𝑒𝑛 𝑑𝑎𝑦𝑠

                       𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑦𝑠

60 + 62 + 61 + 60 + 59 + 63 + 58

                       7

 = 423

     7

=60.42

 Average number of jumps per minute = 60.42 We know that the number of jumps will be counted in natural numbers. Never will there be a fractional number of jumps. However, their average can be a fractional number.

Q.2 The annual rainfall of Mumbai is given below.

What is the average rainfall for those 5 years. 900mm,600mm,340mm,1000mm,850mm.

Solution : 𝑆𝑢𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑗𝑢𝑚𝑝𝑠 𝑜𝑛 𝑠𝑒𝑣𝑒𝑛 𝑑𝑎𝑦𝑠

                     𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑦𝑠

 = 900 + 600 + 340 + 1000 + 850

                 5

 3690

    5

= 738

 The average rainfall in Mumbai is 738mm.

𝟐. Frequency Distribution Table

 The number of times a particular score occurs in a data is called the 3 frequency of that score. In such cases a frequency table is made with three columns, one each for the score, the tally marks and the frequency.

1. In the first column, scores are entered in ascending order. For example, enter 1, 2, 3, 4, 5, 6 in order one below the other.

 2. Read the scores in the data in serial order and enter a tally mark ‘।’ for each in the second column of the table in front of that score, e.g. if you read the score ‘3’, make a tally mark in front of 3 in the second column. Place four tally marks like this ।।।।, but make the fifth one like this ।।।।. It makes it easier to count the total number of tally marks.

 3. Count the total number of tally marks in front of each score and enter the number in the next, i.e. third, column. This number is the frequency of the score.

4. Lastly, add all the frequencies. Their sum is denoted by the letter N. This sum is equal to the total number of scores.

A simple way to tabulate scores is by using tally marks. A table in which the number of tally marks indicates the frequency is called a frequency table. When the number of scores is very large, a frequency table is used to find their average.

Q.1 The marks of 20 students in Maths are given below.Prepare a frequency table. 10,12,10,12,15,15,12,14,18,12,13,16,19,13,19,20,18,19,17,20.

Solution

* Q.2. Priya’s mother bought some peas and began to shell them. Priya was sitting nearby studying her maths lesson and she observed that some of the peapods had just 4 peas while some had 7. So, she took 50 of the pods and, as she shelled them, she noted down the number of peas in each of the pods. 4, 3, 2, 4, 3, 4, 3, 3, 2, 8 2, 3, 3, 4, 3, 4, 4, 5, 2, 8 8, 2, 5, 3, 4, 4, 3, 6, 2, 3 4, 4, 3, 3, 2, 6, 4, 4, 7, 2 3, 6, 3, 6, 6, 6, 7, 6, 7, 3

Prepare Frequency Table

Solution