The group frequency table showing distribution of weights of packets of butter is:
\begin{tabular}{|c|c|c|} \hline Weight in grams & Tally & Frequency \\ \hline $110.5-$ under 112.5 & III & 3 \\ $112.5-$ under 114.5 & III & 5 \\ $114.5-$ under 116.5 & III II & 7 \\ $116.5-$ under 118.5 & III III & 8 \\ $118.5-$ under 120.5 & III & 3 \\ \hline \end{tabular}
The weight written on each packet was 116.5 g. How many packets were under this weight?
Answer (2)
Identify the weight classes strictly less than 116.5g.
Note the frequencies of these classes: 3, 5, and 7.
Sum the frequencies: 3 + 5 + 7 = 15 .
The number of packets under 116.5g is 15 .
Explanation
Understand the problem We are given a frequency table that shows the distribution of weights of butter packets. The table is divided into weight intervals, and we need to find out how many packets weigh less than 116.5g.
Identify relevant intervals The weight intervals are:
110.5 - under 112.5
112.5 - under 114.5
114.5 - under 116.5
116.5 - under 118.5
118.5 - under 120.5
We need to consider only the intervals where the weights are under 116.5g. These are the first three intervals.
List the frequencies The frequencies for these intervals are:
110.5 - under 112.5: 3
112.5 - under 114.5: 5
114.5 - under 116.5: 7
To find the total number of packets under 116.5g, we add these frequencies together.
Calculate the total So, the total number of packets under 116.5g is 3 + 5 + 7 = 15 .
State the answer Therefore, there are 15 packets of butter that weigh less than 116.5g.
Examples
In quality control for food packaging, it's crucial to ensure that products meet weight standards. This type of calculation helps manufacturers determine how many products fall below a certain weight threshold, allowing them to adjust their processes and avoid regulatory issues or customer dissatisfaction. For example, a company producing snack bars might use this method to check if the number of underweight bars is within acceptable limits. By analyzing the frequency distribution of weights, they can quickly identify and address any problems in their production line, ensuring that most products meet the labeled weight.
There are 15 packets of butter that weigh less than 116.5 grams based on the frequency table. This was determined by adding the frequencies of the intervals that are below 116.5 grams. The sum of these frequencies is 15, indicating how many packets fall below this weight threshold.
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