Question

which data set has a mean of 35, median of 32, and a mode of 47?
75, 35, 19, 20, 21, 25, 26, 35, 35
68, 52, 9, 16, 48, 19, 48, 26, 50
70, 60, 50, 80, 70, 32, 35, 35, 35
68, 53, 10, 15, 47, 18, 47, 25, 32
question #2
find the median of the data set
18, 36, 24, 36, 30 and 36
35
33
30
36

Explanation:

Step1: Recall mean, median and mode formulas

Mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, median is middle - value (for odd $n$) or average of two middle - values (for even $n$) after arranging data in ascending order, mode is the most frequently occurring value.

Step2: Check first option for mean, median and mode

For data set $75,35,19,20,21,25,26,35,35$:

• Mean: $\bar{x}=\frac{75 + 35+19+20+21+25+26+35+35}{9}=\frac{291}{9}\approx32.33$.
• Arranged in ascending order: $19,20,21,25,26,35,35,35,75$. Median is $26$. Mode is $35$. This is not the correct set.

Step3: Check second option for mean, median and mode

For data set $68,52,9,16,48,19,48,26,50$:

• Mean: $\bar{x}=\frac{68 + 52+9+16+48+19+48+26+50}{9}=\frac{336}{9}\approx37.33$.
• Arranged in ascending order: $9,16,19,26,48,48,50,52,68$. Median is $48$. Mode is $48$. This is not the correct set.

Step4: Check third option for mean, median and mode

For data set $70,60,50,80,70,32,35,35,35$:

• Mean: $\bar{x}=\frac{70+60 + 50+80+70+32+35+35+35}{9}=\frac{467}{9}\approx51.89$.
• Arranged in ascending order: $32,35,35,35,50,60,70,70,80$. Median is $50$. Mode is $35$. This is not the correct set.

Step5: Check fourth option for mean, median and mode

For data set $68,53,10,15,47,18,47,25,32$:

• Mean: $\bar{x}=\frac{68+53 + 10+15+47+18+47+25+32}{9}=\frac{315}{9}=35$.
• Arranged in ascending order: $10,15,18,25,32,47,47,53,68$. Median is $32$. Mode is $47$. This is the correct set.

For Question #2:

Step1: Arrange data in ascending order

The data set is $18,24,30,36,36,36$.

Step2: Find the median

Since $n = 6$ (even), median $=\frac{30 + 36}{2}=33$.

Answer:

Question #1: Fourth option $68,53,10,15,47,18,47,25,32$
Question #2: $33$