Question

31. Some surnames were picked up from a local telephone directory and the frequency
distribution of the number of letters of the English alphabets was obtained as follows:
35 |
Number of letters
Number of surnames
1-4
10
4-7
25
| 7-10
10-13
13-16
12
16-19
8
It is given that mode of the distribution is 8, then find the missing frequency (x).
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Answer 1

Given: We are provided with the groped data of number of letters of English alphabets. Also the mode of the distribution is 8.

Find: Have to find the missing frequency x.

Step-by-step explanation:

Number of Letters        Number of Surnames            Cumulative Frequency

        1-4                                       10                                          10

        4-7                                      25                                          35

        7-10                                     35                                          70

        10-13                                    x                                            70+x  

        13-16                                    12                                           82+x

         16-19                                   8                                            90+x

                                                N = 90+x

                                              $N=\frac{90+x}{2}\\N=45+\frac{x}{2}$

      Modal Class =  Class with cumulative frequency more or higher than $\frac{N}{2}$

      Modal Class = 7-10

                                     Mode = $l+\frac{f_{1}-f_{0}}{2f_{1}-f_{0}-f{1}}\times h$

where  $l$ = lower limit of the modal class

 $f_{1}$ = frequency of the modal class

 $f_{0}$ = frequency of the class preceding modal class

 $f_{2}$ = frequency of the class succeeding modal class

  $h$ = size of the class

               $8=7+\frac{35-25}{2\times 35- 25-x}\times 3\\8-7=\frac{10}{45-x}\times3\\1=\frac{30}{45-x}\\45-x=30\\x=45-30\\x=15$

Answer: So the missing frequency x = 15.

                       

Answer 2

Answer:

Step-by-step explanation:

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