Question

question #3
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, 53, 10, 15, 47, 18, 47, 25, 32
68, 52, 9, 16, 48, 19, 48, 26, 50
70, 60, 50, 80, 70, 32, 35, 35, 35

Explanation:

Step1: Sort the data sets

Sort each data set in ascending order.

• For the first data set \(19,20,21,25,26,35,35,35,75\).
• For the second data set \(10,15,18,25,32,47,47,53,68\).
• For the third data set \(9,16,19,26,48,48,50,52,68\).
• For the fourth data set \(32,35,35,35,50,60,70,70,80\).

Step2: Calculate the mean

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 9\).

• First data set: \(\frac{19+20+21+25+26+35+35+35+75}{9}=\frac{291}{9}\approx32.33\).
• Second data set: \(\frac{10 + 15+18+25+32+47+47+53+68}{9}=\frac{315}{9}=35\).
• Third data set: \(\frac{9+16+19+26+48+48+50+52+68}{9}=\frac{336}{9}\approx37.33\).
• Fourth data set: \(\frac{32+35+35+35+50+60+70+70+80}{9}=\frac{467}{9}\approx51.89\).

Step3: Find the median

The median is the middle - value (\(n = 9\), so the 5th value).

• First data set: \(26\).
• Second data set: \(32\).
• Third data set: \(48\).
• Fourth data set: \(50\).

Step4: Find the mode

The mode is the most - frequently occurring value.

• First data set: \(35\).
• Second data set: \(47\).
• Third data set: \(48\).
• Fourth data set: \(35\).

Answer:

\(68,53,10,15,47,18,47,25,32\)