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

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.

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Similar questions

Q. A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:

\begin{matrix} 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 \end{matrix}

Construct a grouped frequency distribution table for this data, using class intervals of size

0.5

starting from the interval

2 - 2.5

Q. A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:

\begin{matrix} 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 \end{matrix}

Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the intervals 2−2.5.

A company manufactures car batteries of a particular type. The lives (in years) of 40 such 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 for this data, using class intervals of size 0.5 starting from the intervals 2 − 2.5.

Q. Question 9
A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:

\begin{matrix} 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 \end{matrix}

Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the intervals 2−2.5.

A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:
$\begin{matrix} 2.6 & 3.0 & 3.7 & 3.2 & 2.2 & 4.1 & 3.5 & 4.5 3.5 & 2.3 & 3.2 & 3.4 & 3.8 & 3.2 & 4.6 & 3.7 2.5 & 4.4 & 3.4 & 3.3 & 2.9 & 3.0 & 4.3 & 2.8 3.5 & 3.2 & 3.9 & 3.2 & 3.2 & 3.1 & 3.7 & 3.4 4.6 & 3.8 & 3.2 & 2.6 & 3.5 & 4.2 & 2.9 & 3.6 \end{matrix}$

The number of batteries having a life of 3.5-4.0 years is:
(Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the intervals 2−2.5)

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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