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 five cars; nineteen generally sell six cars; twelve generally sell seven cars; nine generally sell eight cars; eleven generally sell nine cars. Use this information to calculate the following value. (Enter an exact number as an integer, fraction, or decimal.)

What is the Third quartile?

Answer 1

The third quartile (Q3) of the number of cars sold by salespersons in a week is six cars, which is the value below which 75% of the data falls.

Step-by-step explanation:

To find the third quartile (Q3) of the data representing the number of cars sold by salespersons in a week, we first need to organize the data and determine the position of Q3. The number of cars sold can be arranged as follows: 14 salespersons sold three cars, 19 sold four cars, 12 sold five cars, 9 sold six cars, and 11 sold seven cars. To find Q3, which is the value below which 75% of the data falls, we can use the formula for the position P of a given percentile, which is: P = (n + 1) * (percentile / 100) where n is the total number of observations. In this case, n = 65, so P = (65+1) * (75 / 100) = 66 * 0.75 = 49.5. Since the position is a decimal, we take the average of the 49th and 50th values.

By adding the cumulative frequencies (14+19=33 for three and four cars, 33+12=45 for five cars, 45+9=54 for six cars), we can see that the 49th and 50th values both fall within the group that generally sells six cars a week. Therefore, the third quartile Q3 is six cars, as this is the number below which 75% of the salespersons' sales fall.