Question

:
50
35
9. A box contains nails of different lengths, measured to the nearest half centimetres : the frequency distribution is
as follows:
Length (class mark)
2.5 3 3.5 4 4.5 5
No. of nails (frequency) 10 35
45
25
Cumulative frequency
10 45 95 140 175 200
(1) State the upper boundary of the last class :
(1) State the class size :
(ii) State the modal class :
(iv) Determine the class which contains the median of the distribution.
(ICSE)​

Answer 1

Step-by-step explanation:

make the class interval with the help of adjustment factor. remaining as shown and given in the figure.

Answer 2

1. The upper boundary of the last class is 5.25.

2. 0.5 is the class interval.

3. The model class is 3.25 - 3.75

4. The class which contains the median of the distribution is 3.75 - 4.25.

Given that,

A box contains nails of different lengths, measured to the nearest half centimeters, the frequency distribution.

We know that,

Class varies         frequency       cumulative           class interval

                                                    frequency(cf)

   2.5                         10                    10                         2.25 - 2.75

   3                            35                   45                         2.75 - 3.25

  3.5                          50                   95                         3.25 - 3.75

   4                            35                   140                        3.75 - 4.25    

  4.5                          45                   175                        4.25 - 4.75

   5                            25                   200                       4.75 - 5.25

1. The upper boundary of the last class

The last class interval is 4.75 - 5.25 and the upper boundary is 5.25.

2. The class size

The class size we find by the difference of the class intervals

2.25 - 2.75 = 0.5

2.75 - 3.25 = 0.5

So, 0.5 is the class interval.

3. The modal class

The model class we get from the highest frequency

The highest frequency is 50 which has class interval 3.25 - 3.75

The model class is 3.25 - 3.75

4. Median for n = 200 even

Median = $\frac{n+1}{2}$ = $\frac{200+1}{2}$ = 100.5th

The term lies at cumulative frequency value at 140 so the class is 3.75 - 4.25    

Therefore, The class which contains the median of the distribution is 3.75 - 4.25.

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