use the display of data to find the mean, median, mode, and midrange. the mean of the data is. (round to the…

Explanation:

Step1: Find the data - frequency pairs

From the graph:

• Score 9 has frequency 1
• Score 10 has frequency 1
• Score 11 has frequency 3
• Score 12 has frequency 4
• Score 13 has frequency 5
• Score 14 has frequency 6
• Score 15 has frequency 2
• Score 16 has frequency 1

Step2: Calculate the sum of the products of scores and frequencies

[ \begin{align*} \sum_{i}x_if_i&=(9\times1)+(10\times1)+(11\times3)+(12\times4)+(13\times5)+(14\times6)+(15\times2)+(16\times1)\ &=9 + 10+33+48+65+84+30+16\ &=295 \end{align*} ]

Step3: Calculate the total frequency

[ \begin{align*} n&=1 + 1+3+4+5+6+2+1\ &=23 \end{align*} ]

Step4: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i}x_if_i}{n}=\frac{295}{23}\approx12.8$

Step5: Find the median

Since $n = 23$ (odd), the median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{23+1}{2}=12$-th value. Counting the frequencies: $1+1+3+4 = 9$ (first 9 values), and adding the frequency of 13 (5 values), we get to the 14 - th value when considering scores up to 13. So the median is 13.

Step6: Find the mode

The mode is the score with the highest frequency. The score 14 has the highest frequency of 6, so the mode is 14.

Step7: Find the mid - range

The mid - range is $\frac{\text{Minimum value}+\text{Maximum value}}{2}=\frac{9 + 16}{2}=\frac{25}{2}=12.5$

Answer:

Mean: 12.8 Median: 13 Mode: 14 Mid - range: 12.5