Question

Age at death of 50 persons of a town are given below: 36, 48, 50, 45, 49, 31, 50, 48, 43, 42, 37, 32, 40, 39, 41, 47, 45, 39, 43, 47, 38, 39, 37, 40, 32 52, 56, 31, 54, 36, 51, 46, 41, 55, 58, 31, 42, 53, 32, 44, 53, 36, 60, 59, 41, 53, 58, 36, 38, 60 (a) Arrange the data in a frequency distribution in 10 class intervals. (b)Obtain the relative frequency of each class.
Question from statistics

Answer 1

Step-by-step explanation:

36, 48, 50, 45, 49, 31, 50, 48, 43, 42, 37, 32, 40, 39,… ... 39, 41, 47, 45, 39, 43, 47, 38, 39, 37, 40, 32 52, 56, 31, 54, 36, ...

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Answer 2

Given: Age of death of 50 persons of a town are: 36, 48, 50, 45, 49, 31, 50, 48, 43, 42, 37, 32, 40, 39, 41, 47, 45, 39, 43, 47, 38, 39, 37, 40, 32 52, 56, 31, 54, 36, 51, 46, 41, 55, 58, 31, 42, 53, 32, 44, 53, 36, 60, 59, 41, 53, 58, 36, 38, 60.

To find:

(a) Arranged data in a frequency distribution in 10 class intervals.

(b) Relative frequency of each class.

Solution:

(a)

The number of times a value occurs in data is called its frequency.

A frequency distribution shows the actual number of observations falling in each range.

To arrange the data in a frequency distribution in 10 class intervals,

• Firstly, find the lowest and the highest value of the variable. As in our case, 31 is the lowest value and 60 is the highest value.
• Next, we need to decide the class intervals. As it is given to make 10 class intervals, so from 31 to 60, if we take each class interval of 3, we will get 10 class intervals.
• Lastly, all possible values of the variables in their respective class intervals.

   Age of death (x)                        frequency (f)

        31-33                                             6

        34-36                                            4

        37-39                                            7

         40-42                                          7

         43-45                                          5

         46-48                                          5

         49-51                                           4

        52-54                                           5

        55-57                                           2

         58-60                                         5

        Total                                          50

(b)

Relative frequency is the ratio of the number of times a value occurs to the total number of outcomes.

⇒ Relative frequency = $\frac{frequency of class}{total}$

Thus, relative frequency of each class will be:

Class intervals               Frequency                Relative frequency

   31-33                                  6                              $\frac{6}{50}$ = 0.12

   34-36                                 4                              $\frac{4}{50}$ = 0.08

   37-39                                 7                               $\frac{7}{50}$ = 0.14

   40-42                                 7                              $\frac{7}{50}$ = 0.14

    43-45                                5                              $\frac{5}{50}$ = 0.1

    46-48                                5                              $\frac{5}{50}$ = 0.1

    49-51                                 4                              $\frac{4}{50}$ = 0.08          

    52-54                                5                             $\frac{5}{50}$ = 0.1

    55-57                                2                              $\frac{2}{50}$ = 0.04

    58-60                                5                             $\frac{5}{50}$ = 0.1