Question

simplify:0.2 of (4.59×1.8÷3.6+5.4×1/9_2)​

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A company manufactures car batteries of a particular type. The life (in years) of 40 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 3.4 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 with exclusive classes for this data, using class intervals of size 0.5 starting from the interval 2−2.5

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Solution

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Life (in years)

Number of batteries

2.0-2.5 2

2.5-3.0 6

3.0-3.5 14

3.5-4.0 11

4.0-4.5 4

4.5-5.0 3

Given is the life of 40 batteries in years.

We know that a grouped frequency distribution table has class-intervals or groups and their corresponding frequencies.

It is given that the class size needs to be 0.5 and the class intervals must start with 2−2.5.

Also, 4.6 is the highest value in the given data.

Hence, our class intervals will be 2−2.5, 2.5−3, 3−3.5, 3.5−4, 4−4.5 and 4.5−5.

Also, the classes are exclusive. It means the upper limit of a class is excluded from that class (and is included in the next class).

So, the grouped frequency distribution table for the given data will be as shown above.