mathematics. math 003. fall 2025\nunit 4 - statistics\nuse the frequency distribution table to find the a…

mathematics. math 003. fall 2025\nunit 4 - statistics\nuse the frequency distribution table to find the a. mean, b. median, and c. mode.\ndata item frequency data item frequency\n7 1 10 5\n8 1 11 6\n9 2 12 2\na. the mean is . (type a whole number or decimal rounded to one decimal place as needed.)\nb. the median is . (type a whole number or decimal rounded to one decimal place as needed.)\nc. select the correct answer below and, if necessary, fill in the answer box to complete your choice.\na. the mode(s) is/are (type a whole number or decimal rounded to one decimal place as needed. use a comma to separate answers as needed.)\nb. there are no modes.

mathematics. math 003. fall 2025\nunit 4 - statistics\nuse the frequency distribution table to find the a. mean, b. median, and c. mode.\ndata item frequency data item frequency\n7 1 10 5\n8 1 11 6\n9 2 12 2\na. the mean is . (type a whole number or decimal rounded to one decimal place as needed.)\nb. the median is . (type a whole number or decimal rounded to one decimal place as needed.)\nc. select the correct answer below and, if necessary, fill in the answer box to complete your choice.\na. the mode(s) is/are (type a whole number or decimal rounded to one decimal place as needed. use a comma to separate answers as needed.)\nb. there are no modes.

Answer

Explanation:

Step1: Calculate the sum of the products of data items and frequencies

First, find the product of each data - item and its frequency: For data item 7 with frequency 1: $7\times1 = 7$ For data item 8 with frequency 1: $8\times1=8$ For data item 9 with frequency 2: $9\times2 = 18$ For data item 10 with frequency 5: $10\times5=50$ For data item 11 with frequency 6: $11\times6 = 66$ For data item 12 with frequency 2: $12\times2=24$ The sum of the products $\sum_{i}x_{i}f_{i}=7 + 8+18+50+66+24=173$ The total frequency $n=\sum_{i}f_{i}=1 + 1+2+5+6+2=17$ The mean $\bar{x}=\frac{\sum_{i}x_{i}f_{i}}{n}=\frac{173}{17}\approx10.2$

Step2: Find the median

Arrange the data in ascending order with their frequencies. The total number of data points $n = 17$ (an odd - numbered data set). The median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{17+1}{2}=9$ - th value. Count the frequencies: $1$ (for 7) + $1$ (for 8)+$2$ (for 9)=$4$, $4 + 5$ (for 10)=$9$. So the median is 10.

Step3: Find the mode

The mode is the data item with the highest frequency. The frequency of 11 is 6, which is the highest among all frequencies. So the mode is 11.

Answer:

a. 10.2 b. 10 c. A. 11