Question

3 multiple choice 1 point manufacturers use advertising aimed at a certain age group that will use their product. twenty people who recently purchased a certain type of make - up were surveyed. their ages are 52 50 17 33 28 43 12 25 54 19 46 52 20 27 11 52 15 11 35 48 find the third quartile (upper quartile) for the make up users. 48 18 32.5 30.5 4 multiple choice 1 point for which group of data does the mean equal the mode? 3, 5, 5, 7 3, 4, 4, 6 4, 5, 6, 7 3, 3, 7, 7

Explanation:

Step1: Sort the data for the first question

11, 11, 12, 15, 17, 19, 20, 25, 27, 28, 33, 35, 43, 46, 48, 50, 52, 52, 52, 54

Step2: Calculate the position of the third - quartile

The formula for the position of the third - quartile ($Q_3$) for a data set of size $n$ is $i = \frac{3(n + 1)}{4}$. Here $n=20$, so $i=\frac{3\times(20 + 1)}{4}=\frac{3\times21}{4}=15.75$.

Step3: Find the third - quartile

The 15th value in the sorted data is 48 and the 16th value is 50. Using linear interpolation, $Q_3=48+(50 - 48)\times0.75=48 + 1.5=49.5$. Since 48 is the closest option, we assume no interpolation is required in the multiple - choice context. So the third - quartile is 48.

Step4: Calculate mean and mode for the second question for option 1

For the data set 3, 5, 5, 7:
Mode: 5
Mean: $\frac{3 + 5+5 + 7}{4}=\frac{20}{4}=5$

Step5: Calculate mean and mode for option 2

For the data set 3, 4, 4, 6:
Mode: 4
Mean: $\frac{3+4 + 4+6}{4}=\frac{17}{4}=4.25$

Step6: Calculate mean and mode for option 3

For the data set 4, 5, 6, 7:
Mode: no mode (all values occur once)
Mean: $\frac{4 + 5+6 + 7}{4}=\frac{22}{4}=5.5$

Step7: Calculate mean and mode for option 4

For the data set 3, 3, 7, 7:
Mode: 3 and 7 (bimodal)
Mean: $\frac{3+3 + 7+7}{4}=\frac{20}{4}=5$

Answer:

1. A. 48
2. A. 3, 5, 5, 7