Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Use this information to calculate the following value. (Enter an exact number as an integer, fraction, or decimal.)First quartile cars
Question
Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Use this information to calculate the following value. (Enter an exact number as an integer, fraction, or decimal.)First quartile cars
Solution
To calculate the first quartile, we first need to understand that the first quartile (Q1) is the middle number between the smallest number and the median of the data set. It is also known as the 25th percentile.
The total number of car salespersons is 65.
First, we need to arrange the data in ascending order: 3, 4, 5, 6, 7.
Then, we calculate the position of the first quartile using the formula: Q1 position = (1/4) * (n + 1) where n is the total number of observations.
Q1 position = (1/4) * (65 + 1) = 16.5
Since we have a fractional number, we take the average of the 16th and 17th values in our data set.
Looking at the data, the 16th and 17th salespersons both fall into the category of those who sell 4 cars. So, the first quartile or Q1 is 4 cars.
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