Question

4.
The length of time taken by each of 18 workers to complete a specific job wa
observed to be the following:
5-9
Timeſin min)
5-9,10-14,15-19,20-24,25-29
No. of workers
3,8,4,2,1
Calculate the median time and Q1, and Q3
the fline data.​

Answer 1

The median time is 12.

To calculate the median time,

we need to find the middle value in the data set when it is arranged in numerical order.

Since there are 18 workers in total, we can find the median by identifying the 9th value (the middle value) in the set.

The time intervals are not continuous values, but are ranges of time, so we can use the midpoint of the interval:

5-9 (7), 10-14(12), 15-19(17), 20-24(22), 25-29(27)

From the given data, we can see that the first 8 values (3+8) are less than or equal to 12. And the 9th value is 17. Therefore, the median time is 12.

To calculate Q1, we need to find the value at the 25th percentile in the dataset (the first quartile).

Since there are 18 workers, we need to find the value that separates the lowest 25% of the data from the rest. From the given data, we can see that the first 3 values are less than or equal to 7. Therefore, Q1 is 7.

To calculate Q3, we need to find the value at the 75th percentile in the dataset (the third quartile).

Since there are 18 workers, we need to find the value that separates the highest 25% of the data from the rest. From the given data, we can see that the last 4 values (2+1) are greater than or equal to 22. Therefore, Q3 is 22.

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