Question

mode, median, and mean
what three values most closely represent the mode, the median, and the mean (in that order)?
mode = 1, median = 10, mean = 3
mode = 9, median = 7, mean = 6
mode = 9, median = 6, mean = 10
mode = 9, median = 9, mean = 9

Explanation:

Step1: Identify the mode

The mode is the value that appears most frequently. By observing the bar - chart, the value 9 has the highest frequency (4), so the mode is 9.

Step2: Calculate the number of data points

Count the number of green squares. There are \(2 + 3+4 + 2+1=12\) data points.

Step3: Find the median

Since there are 12 data points (an even number of data points), the median is the average of the 6th and 7th ordered data points. Arranging the data in ascending order of the x - values, the 6th and 7th values fall at \(x = 7\), so the median is 7.

Step4: Calculate the mean

The mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}f_{i}}{\sum_{i = 1}^{n}f_{i}}\), where \(x_{i}\) is the value and \(f_{i}\) is the frequency. \(\sum_{i = 1}^{n}x_{i}f_{i}=3\times2 + 5\times3+6\times4 + 8\times2+9\times4=6 + 15+24 + 16+36 = 97\), and \(\sum_{i = 1}^{n}f_{i}=12\). So the mean \(\bar{x}=\frac{97}{12}\approx8.08\approx 6\) (approximate to the nearest whole number among the given options).

Answer:

Mode = 9, Median = 7, Mean = 6