Question

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

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)

• A. 6
• B. 4
• C. 11
• D. 14

Answer 1

The correct option is C

11

A grouped frequency table of class size 0.5 has to be constructed, starting from class interval 2 − 2.5.
Therefore, the class intervals will be 2−2.5, 2.5 −3, 3− 3.5…
By observing the data given above, the required grouped frequency distribution table can be constructed as follows.
$\begin{array}{cc}\text{Lives of batteries(in years)}& \text{Number of batteries}\\ 2-2.5& 2\\ 2.5-3.0& 6\\ 3.0-3.5& 14\\ 3.5-4.0& 11\\ 4.0-4.5& 4\\ 4.5-5.0& 3\\ Total& 40\end{array}$

From the above grouped frequency distribution table, we find that the number of batteries having a life of 3.5-4.0 years is 11.